Risky + Safe Asset (Saving Only) Interpolated-Percentage (Loop)

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Contents

function result_map = ff_ipwkz_vf(varargin)

FF_IPWKZ_VF solve infinite horizon exo shock + endo asset problem

This program solves the infinite horizon dynamic savings and risky capital asset problem. This is the two step solution with interpolation and with percentage asset grids version of ff_akz_vf. See ff_wkz_vf for details about the second stage. See ff_iwkz_vf for details about interpolation over u(c) and value(coh,z). The new ingredient here is the use of percentage choice grid rather than level choice grid. This is the looped code.

@param param_map container parameter container

@param support_map container support container

@param armt_map container container with states, choices and shocks grids that are inputs for grid based solution algorithm

@param func_map container container with function handles for consumption cash-on-hand etc.

@return result_map container contains policy function matrix, value function matrix, iteration results, and policy function, value function and iteration results tables.

keys included in result_map:

@example

@include

Default

it_param_set = 4;
bl_input_override = true;
[param_map, support_map] = ffs_ipwkz_set_default_param(it_param_set);

% parameters can be set inside ffs_ipwkz_set_default_param or updated here
param_map('it_w_perc_n') = 10;
% param_map('it_ak_perc_n') = param_map('it_w_perc_n');
param_map('it_z_n') = 5;
% param_map('fl_coh_interp_grid_gap') = 0.025;
% param_map('it_c_interp_grid_gap') = 0.001;
% param_map('fl_w_interp_grid_gap') = 0.25;
% param_map('it_w_perc_n') = 100;
% param_map('it_ak_perc_n') = param_map('it_w_perc_n');
% param_map('it_z_n') = 11;
param_map('fl_coh_interp_grid_gap') = 0.5;
% param_map('it_c_interp_grid_gap') = 10^-4;
param_map('fl_w_interp_grid_gap') = 0.5;

% get armt and func map
[armt_map, func_map] = ffs_ipwkz_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override
default_params = {param_map support_map armt_map func_map};

Parse Parameters 1

% if varargin only has param_map and support_map,
params_len = length(varargin);
[default_params{1:params_len}] = varargin{:};
param_map = [param_map; default_params{1}];
support_map = [support_map; default_params{2}];
if params_len >= 1 && params_len <= 2
    % If override param_map, re-generate armt and func if they are not
    % provided
    bl_input_override = true;
    [armt_map, func_map] = ffs_ipwkz_get_funcgrid(param_map, support_map, bl_input_override);
else
    % Override all
    armt_map = [armt_map; default_params{3}];
    func_map = [func_map; default_params{4}];
end

% append function name
st_func_name = 'ff_ipwkz_vf';
support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];
support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];
support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

Parse Parameters 2

% armt_map
params_group = values(armt_map, {'ar_w_perc', 'ar_w_level', 'ar_z'});
[ar_w_perc, ar_w_level, ar_z] = params_group{:};
params_group = values(armt_map, {'ar_interp_c_grid', 'ar_interp_coh_grid', ...
    'mt_interp_coh_grid_mesh_z', 'mt_z_mesh_coh_interp_grid',...
    'mt_w_by_interp_coh_interp_grid'});
[ar_interp_c_grid, ar_interp_coh_grid, ...
    mt_interp_coh_grid_mesh_z, mt_z_mesh_coh_interp_grid, ...
    mt_w_by_interp_coh_interp_grid] = params_group{:};
params_group = values(armt_map, {'mt_coh_wkb', 'mt_z_mesh_coh_wkb'});
[mt_coh_wkb, mt_z_mesh_coh_wkb] = params_group{:};

% func_map
params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons'});
[f_util_log, f_util_crra, f_cons] = params_group{:};

% param_map
params_group = values(param_map, {'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min'});
[it_z_n, fl_crra, fl_beta, fl_c_min] = params_group{:};
params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});
[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};

% support_map
params_group = values(support_map, {'bl_profile', 'st_profile_path', ...
    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...
    'bl_time', 'bl_graph_evf', 'bl_display', 'it_display_every', 'bl_post'});
[bl_profile, st_profile_path, ...
    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...
    bl_time, bl_graph_evf, bl_display, it_display_every, bl_post] = params_group{:};

Initialize Output Matrixes

mt_val_cur = zeros(length(ar_interp_coh_grid),length(ar_z));
mt_val = mt_val_cur - 1;
mt_pol_a = zeros(length(ar_interp_coh_grid),length(ar_z));
mt_pol_a_cur = mt_pol_a - 1;
mt_pol_k = zeros(length(ar_interp_coh_grid),length(ar_z));
mt_pol_k_cur = mt_pol_k - 1;

Initialize Convergence Conditions

bl_vfi_continue = true;
it_iter = 0;
ar_val_diff_norm = zeros([it_maxiter_val, 1]);
ar_pol_diff_norm = zeros([it_maxiter_val, 1]);
mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

Pre-calculate u(c)

Interpolation, see fs_u_c_partrepeat_main for why interpolate over u(c)

% Evaluate
if (fl_crra == 1)
    ar_interp_u_of_c_grid = f_util_log(ar_interp_c_grid);
    fl_u_neg_c = f_util_log(fl_c_min);
else
    ar_interp_u_of_c_grid = f_util_crra(ar_interp_c_grid);
    fl_u_neg_c = f_util_crra(fl_c_min);
end
ar_interp_u_of_c_grid(ar_interp_c_grid <= fl_c_min) = fl_u_neg_c;

% Get Interpolant
f_grid_interpolant_spln = griddedInterpolant(ar_interp_c_grid, ar_interp_u_of_c_grid, 'spline');

Iterate Value Function

Loop solution with 4 nested loops

  1. loop 1: over exogenous states
  2. loop 2: over endogenous states
  3. loop 3: over choices
  4. loop 4: add future utility, integration--loop over future shocks
% Start Profile
if (bl_profile)
    close all;
    profile off;
    profile on;
end

% Start Timer
if (bl_time)
    tic;
end

% Value Function Iteration
while bl_vfi_continue
    it_iter = it_iter + 1;

Interpolate (1) reacahble v(coh(k(w,z),b(w,z),z),z) given v(coh, z)

v(coh,z) solved on ar_interp_coh_grid, ar_z grids, see ffs_ipwkz_get_funcgrid.m. Generate interpolant based on that, Then interpolate for the coh reachable levels given the k(w,z) percentage choice grids in the second stage of the problem

    % Generate Interpolant for v(coh,z)
    f_grid_interpolant_value = griddedInterpolant(...
        mt_z_mesh_coh_interp_grid', mt_interp_coh_grid_mesh_z', mt_val_cur', 'linear', 'nearest');

    % Interpoalte for v(coh(k(w,z),b(w,z),z),z)
    mt_val_wkb_interpolated = f_grid_interpolant_value(mt_z_mesh_coh_wkb, mt_coh_wkb);

Solve Second Stage Problem k*(w,z)

This is the key difference between this function and ffs_akz_set_functions which solves the two stages jointly Interpolation first, because solution coh grid is not the same as all points reachable by k and b choices given w.

    support_map('bl_graph_evf') = false;
    if (it_iter == (it_maxiter_val + 1))
        support_map('bl_graph_evf') = bl_graph_evf;
    end

    bl_input_override = true;
    [mt_ev_condi_z_max, ~, mt_ev_condi_z_max_kp, ~] = ...
        ff_ipwkz_evf(mt_val_wkb_interpolated, param_map, support_map, armt_map, bl_input_override);

Solve First Stage Problem w*(z) given k*(w,z)

loop 1: over exogenous states

    for it_z_i = 1:length(ar_z)

        % Get 2nd Stage Arrays
        ar_ev_condi_z_max_z = mt_ev_condi_z_max(:, it_z_i);
        ar_w_level_kstar_z = mt_ev_condi_z_max_kp(:, it_z_i);

        % Interpolant (2) k*(ar_w_perc) from k*(ar_w_level,z)
        % There are two w=k'+b' arrays. ar_w_level is the level even grid based
        % on which we solve the 2nd stage problem in ff_ipwkz_evf.m. Here for
        % each coh level, we have a different vector of w levels, but the same
        % vector of percentage ws. So we need to interpolate to get the optimal
        % k* and b* choices at each percentage level of w.
        f_interpolante_w_level_kstar_z = griddedInterpolant(ar_w_level, ar_w_level_kstar_z', 'linear', 'nearest');

        % Interpolant for (3) EV(k*(ar_w_perc),Z)
        f_interpolante_ev_condi_z_max_z = griddedInterpolant(ar_w_level, ar_ev_condi_z_max_z', 'linear', 'nearest');

        % loop 2: over endogenous states
        for it_coh_interp_j = 1:length(ar_interp_coh_grid)
            % Get cash-on-hand which include k,b,z
            fl_coh = mt_interp_coh_grid_mesh_z(it_coh_interp_j, it_z_i);

            % loop 3: over choices, only w vector
            % we choose w(z), know from ff_wkz_evf k*(w,z), b*=w-k*
            % fl_w_level_perc_z is the level of w given coh and z based on
            % the w percentage grid generated in ffs_akz_get_funcgrid.m
            ar_val_cur = zeros(size(ar_w_perc));
            ar_w_kstar_z = zeros(size(ar_w_perc));
            ar_w_astar_z = zeros(size(ar_w_perc));
            for it_cohp_k = 1:length(ar_w_perc)

                % Interpolate (2) to get optimal k at current percentage grid
                % level given coh and z
                fl_w_level_perc_z = mt_w_by_interp_coh_interp_grid(it_cohp_k, it_coh_interp_j);
                fl_w_kstar_interp_z = f_interpolante_w_level_kstar_z(fl_w_level_perc_z);
                fl_w_astar_interp_z = fl_w_level_perc_z - fl_w_kstar_interp_z;

                % store optimal interpolated k and a choices given w
                ar_w_kstar_z(it_cohp_k) = fl_w_kstar_interp_z;
                ar_w_astar_z(it_cohp_k) = fl_w_astar_interp_z;

                % consumption
                fl_c = f_cons(fl_coh, fl_w_astar_interp_z, fl_w_kstar_interp_z);

                % Interpolate (3) EV(k*(ar_w_perc),Z)
                fl_ev_condi_z_max_interp_z = f_interpolante_ev_condi_z_max_z(fl_w_level_perc_z);

                % Interpolate (4) consumption
                ar_val_cur(it_cohp_k) = f_grid_interpolant_spln(fl_c) + fl_beta*fl_ev_condi_z_max_interp_z;

                % Replace if negative consumption
                if fl_c <= 0
                    ar_val_cur(it_cohp_k) = fl_u_neg_c;
                end

            end

            % maximization over loop 3 choices for loop 1+2 states
            it_max_lin_idx = find(ar_val_cur == max(ar_val_cur));
            mt_val(it_coh_interp_j,it_z_i) = ar_val_cur(it_max_lin_idx(1));
            mt_pol_a(it_coh_interp_j,it_z_i) = ar_w_astar_z(it_max_lin_idx(1));
            mt_pol_k(it_coh_interp_j,it_z_i) = ar_w_kstar_z(it_max_lin_idx(1));

        end
    end

Check Tolerance and Continuation

    % Difference across iterations
    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur);
    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur) + norm(mt_pol_k - mt_pol_k_cur);
    ar_pol_a_perc_change = sum((mt_pol_a ~= mt_pol_a_cur))/length(ar_interp_coh_grid);
    ar_pol_k_perc_change = sum((mt_pol_k ~= mt_pol_k_cur))/length(ar_interp_coh_grid);
    mt_pol_perc_change(it_iter, :) = mean([ar_pol_a_perc_change;ar_pol_k_perc_change]);

    % Update
    mt_val_cur = mt_val;
    mt_pol_a_cur = mt_pol_a;
    mt_pol_k_cur = mt_pol_k;

    % Print Iteration Results
    if (bl_display && (rem(it_iter, it_display_every)==0))
        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...
            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));
        tb_valpol_iter = array2table([mean(mt_val_cur,1);...
                                      mean(mt_pol_a_cur,1); ...
                                      mean(mt_pol_k_cur,1); ...
                                      mt_val_cur(length(ar_interp_coh_grid),:); ...
                                      mt_pol_a_cur(length(ar_interp_coh_grid),:); ...
                                      mt_pol_k_cur(length(ar_interp_coh_grid),:)]);
        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));
        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'mak', 'Hval', 'Hap', 'Hak'};
        disp('mval = mean(mt_val_cur,1), average value over a')
        disp('map  = mean(mt_pol_a_cur,1), average choice over a')
        disp('mkp  = mean(mt_pol_k_cur,1), average choice over k')
        disp('Hval = mt_val_cur(ar_interp_coh_grid,:), highest a state val')
        disp('Hap = mt_pol_a_cur(ar_interp_coh_grid,:), highest a state choice')
        disp('mak = mt_pol_k_cur(ar_interp_coh_grid,:), highest k state choice')
        disp(tb_valpol_iter);
    end

    % Continuation Conditions:
    % 1. if value function convergence criteria reached
    % 2. if policy function variation over iterations is less than
    % threshold
    if (it_iter == (it_maxiter_val + 1))
        bl_vfi_continue = false;
    elseif ((it_iter == it_maxiter_val) || ...
            (ar_val_diff_norm(it_iter) < fl_tol_val) || ...
            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol))
        % Fix to max, run again to save results if needed
        it_iter_last = it_iter;
        it_iter = it_maxiter_val;
    end
end

% End Timer
if (bl_time)
    toc;
end

% End Profile
if (bl_profile)
    profile off
    profile viewer
    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];
    profsave(profile('info'), strcat(st_profile_path, st_file_name));
end

Process Optimal Choices

result_map = containers.Map('KeyType','char', 'ValueType','any');
result_map('mt_val') = mt_val;

result_map('cl_mt_pol_coh') = {mt_interp_coh_grid_mesh_z, zeros(1)};
result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)};
result_map('cl_mt_pol_k') = {mt_pol_k, zeros(1)};
result_map('cl_mt_pol_c') = {f_cons(mt_interp_coh_grid_mesh_z, mt_pol_a, mt_pol_k), zeros(1)};
result_map('cl_mt_val') = {mt_val, zeros(1)};
result_map('ar_st_pol_names') = ["cl_mt_val", "cl_mt_coh", "cl_mt_pol_a", "cl_mt_pol_k", "cl_mt_pol_c"];

if (bl_post)
    bl_input_override = true;
    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);
    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);
    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);

    % graphing based on coh_wkb, but that does not match optimal choice
    % matrixes for graphs.
    armt_map('mt_coh_wkb') = mt_interp_coh_grid_mesh_z;
    armt_map('it_ameshk_n') = length(ar_interp_coh_grid);
    armt_map('ar_a_meshk') = mt_interp_coh_grid_mesh_z(:,1);
    armt_map('ar_k_mesha') = zeros(size(mt_interp_coh_grid_mesh_z(:,1)) + 0);

    result_map = ff_akz_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);
end
valgap = norm(mt_val - mt_val_cur): value function difference across iterations
polgap = norm(mt_pol_a - mt_pol_a_cur): policy function difference across iterations
z1 = z1 perc change: (sum((mt_pol_a ~= mt_pol_a_cur))+sum((mt_pol_k ~= mt_pol_k_cur)))/(2*it_ameshk_n):percentage of state space points conditional on shock where the policy function is changing across iterations
                valgap     polgap        z1           z2           z3           z4           z5    
               ________    _______    _________    _________    _________    _________    _________

    iter=1       36.785     48.226            1            1            1            1            1
    iter=2       28.476     415.77            1            1            1            1            1
    iter=3       23.711     171.52      0.99115            1            1      0.99115       0.9823
    iter=4       20.295     54.506      0.30088      0.27434      0.42478      0.70796      0.81416
    iter=5       17.619     80.014      0.87611      0.76106      0.70796      0.49558      0.31858
    iter=6       15.522     34.407      0.10619      0.17699      0.25664      0.26549      0.49558
    iter=7       13.719     15.718     0.053097     0.097345      0.15929      0.15044      0.28319
    iter=8       12.137     9.5078     0.044248      0.10619      0.10619      0.11504      0.18584
    iter=9       10.761     40.481      0.33628      0.21239     0.061947     0.035398     0.088496
    iter=10      9.6255     32.789      0.19469      0.26549      0.25664     0.035398     0.088496
    iter=11      8.6679     26.369     0.088496      0.15929      0.19469      0.16814     0.026549
    iter=12       7.843     22.292     0.044248     0.070796      0.10619      0.15044     0.070796
    iter=13      7.1292       23.6     0.035398     0.035398     0.061947      0.14159      0.18584
    iter=14       6.508     25.163     0.017699     0.026549     0.079646     0.070796      0.18584
    iter=15      5.9561     16.667     0.017699     0.017699     0.026549     0.061947      0.17699
    iter=16      5.4615     11.302    0.0088496     0.053097     0.044248     0.035398      0.19469
    iter=17      5.0153     10.162    0.0088496    0.0088496     0.017699     0.070796     0.079646
    iter=18      4.6109     7.9175     0.053097    0.0088496    0.0088496     0.044248     0.035398
    iter=19      4.2426     7.1609     0.017699     0.035398     0.044248     0.026549     0.044248
    iter=20      3.9074     6.8297    0.0088496            0     0.053097     0.026549     0.035398
    iter=21      3.6019     5.4418            0     0.044248            0     0.053097     0.026549
    iter=22      3.3224     4.8527            0            0     0.026549     0.035398     0.017699
    iter=23       3.067     4.6338            0     0.017699            0     0.026549     0.017699
    iter=24      2.8333     3.2733    0.0088496    0.0088496            0     0.017699    0.0088496
    iter=25       2.619     3.6959            0     0.044248     0.026549     0.017699    0.0088496
    iter=26       2.423     3.7483            0            0    0.0088496            0     0.017699
    iter=27       2.243     3.8526            0            0            0    0.0088496     0.061947
    iter=28       2.078      2.965            0            0            0            0    0.0088496
    iter=29      1.9261      3.729            0            0            0    0.0088496    0.0088496
    iter=30      1.7869          0            0            0            0            0            0
    iter=31      1.6586     2.8528            0            0            0            0    0.0088496
    iter=32      1.5407      3.064            0            0     0.017699    0.0088496            0
    iter=33      1.4322          0            0            0            0            0            0
    iter=34       1.332     3.1215            0            0            0     0.017699     0.026549
    iter=35      1.2396     2.7967     0.017699            0            0            0    0.0088496
    iter=36      1.1543     1.4383            0            0            0     0.017699            0
    iter=37      1.0755     2.0678            0    0.0088496            0            0            0
    iter=38      1.0026     2.7407            0            0            0    0.0088496            0
    iter=39      0.9352          0            0            0            0            0            0
    iter=40     0.87267          0            0            0            0            0            0
    iter=41     0.81473     2.7407            0            0            0            0    0.0088496
    iter=42     0.76099    0.77814            0            0    0.0088496            0            0
    iter=43     0.71108          0            0            0            0            0            0
    iter=44     0.66469     2.4603            0            0    0.0088496            0            0
    iter=45     0.62156          0            0            0            0            0            0
    iter=46     0.58142          0            0            0            0            0            0
    iter=47     0.54404          0            0            0            0            0            0
    iter=48     0.50922    0.67299            0            0            0     0.017699            0
    iter=49     0.47677          0            0            0            0            0            0
    iter=50      0.4465          0            0            0            0            0            0
    iter=51     0.41825          0            0            0            0            0            0
    iter=52     0.39189          0            0            0            0            0            0
    iter=53     0.36726          0            0            0            0            0            0
    iter=54     0.34426          0            0            0            0            0            0
    iter=55     0.32275          0            0            0            0            0            0
    iter=56     0.30265          0            0            0            0            0            0
    iter=57     0.28384          0            0            0            0            0            0
    iter=58     0.26624          0            0            0            0            0            0
    iter=59     0.24977          0            0            0            0            0            0
    iter=60     0.23434          0            0            0            0            0            0
    iter=61      0.2199          0            0            0            0            0            0
    iter=62     0.20638          0            0            0            0            0            0
    iter=63      0.1937          0            0            0            0            0            0
    iter=64     0.18182          0            0            0            0            0            0
    iter=65     0.17069          0            0            0            0            0            0
    iter=66     0.16026          0            0            0            0            0            0
    iter=67     0.15047          0            0            0            0            0            0
    iter=68      0.1413          0            0            0            0            0            0
    iter=69     0.13269          0            0            0            0            0            0
    iter=70     0.12461          0            0            0            0            0            0
    iter=71     0.11704          0            0            0            0            0            0
    iter=72     0.10993          0            0            0            0            0            0
    iter=73     0.10326          0            0            0            0            0            0
    iter=74    0.097002          0            0            0            0            0            0

tb_val: V(a,z) value at each state space point
                            z1_0_33942    z2_0_5596    z3_0_92263    z4_1_5212    z5_2_508
                            __________    _________    __________    _________    ________

    coh1:k=0.443648,b=0       -2.913       -2.0124      -0.93716      0.28775      1.4726 
    coh2:k=0.94931,b=0       0.44426        1.6556        3.0788       4.6197      6.1208 
    coh3:k=1.45497,b=0        1.5724        2.7463        4.1182       5.6359      7.1183 
    coh4:k=1.96063,b=0        2.4036        3.5388        4.8476       6.2841      7.7011 
    coh5:k=2.4663,b=0         3.0225        4.0892        5.3756        6.775      8.1614 
    coh6:k=2.97196,b=0        3.5759        4.6099        5.8288       7.1796      8.5373 
    coh7:k=3.47762,b=0        4.0345         5.035        6.2232       7.5197      8.8506 
    coh8:k=3.98328,b=0        4.4408        5.4084        6.5676       7.8311      9.1147 
    coh9:k=4.48894,b=0        4.8005        5.7374        6.8684       8.1052        9.36 
    coh10:k=4.99461,b=0       5.1173        6.0241        7.1282        8.343      9.5829 
    coh11:k=5.50027,b=0        5.431        6.2863        7.3658       8.5605      9.7865 
    coh12:k=6.00593,b=0       5.7231        6.5248        7.5828       8.7596      9.9723 
    coh13:k=6.51159,b=0        5.997        6.7626        7.7791       8.9433      10.143 
    coh14:k=7.01725,b=0        6.254        6.9941         7.964       9.1185      10.306 
    coh15:k=7.52291,b=0       6.4975        7.2172        8.1675       9.2935      10.462 
    coh16:k=8.02858,b=0       6.7288        7.4311        8.3624       9.4705      10.607 
    coh17:k=8.53424,b=0       6.9492        7.6356        8.5475        9.637      10.745 
    coh18:k=9.0399,b=0        7.1586        7.8302        8.7227       9.7933      10.877 
    coh19:k=9.54556,b=0       7.3575        8.0148        8.8882       9.9403      11.008 
    coh20:k=10.0512,b=0       7.5478        8.1913         9.046        10.08      11.132 
    coh21:k=10.5569,b=0       7.7299        8.3601         9.197       10.213       11.25 
    coh22:k=11.0625,b=0       7.9043        8.5219        9.3417       10.339      11.363 
    coh23:k=11.5682,b=0       8.0703        8.6759        9.4796        10.46      11.469 
    coh24:k=12.0739,b=0         8.23        8.8241         9.612       10.575      11.571 
    coh25:k=12.5795,b=0       8.3839        8.9667        9.7394       10.686      11.669 
    coh26:k=13.0852,b=0       8.5322         9.104        9.8623       10.792      11.764 
    coh27:k=13.5909,b=0       8.6743         9.236        9.9805       10.895      11.854 
    coh28:k=14.0965,b=0        8.811        9.3629        10.094       10.993      11.941 
    coh29:k=14.6022,b=0       8.9434        9.4859        10.204       11.088      12.025 
    coh30:k=15.1078,b=0       9.0718        9.6051        10.311        11.18      12.107 
    coh31:k=15.6135,b=0       9.1962        9.7205        10.415       11.269      12.185 
    coh32:k=16.1192,b=0       9.3155        9.8314        10.514       11.355      12.262 
    coh33:k=16.6248,b=0       9.4386        9.9391        10.611       11.439      12.335 
    coh34:k=17.1305,b=0       9.5592        10.044        10.706       11.521      12.407 
    coh35:k=17.6362,b=0       9.6791        10.146        10.798         11.6      12.477 
    coh36:k=18.1418,b=0       9.7961        10.245        10.887       11.678      12.545 
    coh37:k=18.6475,b=0       9.9108        10.342        10.973       11.753      12.611 
    coh38:k=19.1531,b=0       10.023        10.442        11.057       11.827      12.676 
    coh39:k=19.6588,b=0       10.133        10.542         11.14       11.899      12.739 
    coh40:k=20.1645,b=0       10.242        10.641        11.221       11.969      12.801 
    coh41:k=20.6701,b=0       10.349         10.74        11.299       12.037      12.862 
    coh42:k=21.1758,b=0       10.455        10.836        11.375       12.104      12.922 
    coh43:k=21.6814,b=0        10.56        10.932         11.45        12.17       12.98 
    coh44:k=22.1871,b=0       10.662        11.025        11.523       12.234      13.039 
    coh45:k=22.6928,b=0       10.763        11.117        11.602       12.297      13.097 
    coh46:k=23.1984,b=0       10.862        11.209        11.683       12.359      13.155 
    coh47:k=23.7041,b=0        10.96        11.299        11.765       12.419      13.215 
    coh48:k=24.2098,b=0       11.056        11.389        11.848       12.479      13.277 
    coh49:k=24.7154,b=0        11.15        11.478        11.932       12.558      13.347 
    coh50:k=25.2211,b=0       11.243        11.566        12.016       12.639       13.42 
    coh64:k=32.3003,b=0       12.423        12.704        13.105       13.654      14.332 
    coh65:k=32.806,b=0        12.499        12.778        13.175       13.719       14.39 
    coh66:k=33.3117,b=0       12.574        12.851        13.245       13.783      14.448 
    coh67:k=33.8173,b=0       12.648        12.923        13.313       13.846      14.505 
    coh68:k=34.323,b=0        12.722        12.994        13.381       13.908      14.561 
    coh69:k=34.8287,b=0       12.794        13.064        13.447        13.97      14.616 
    coh70:k=35.3343,b=0       12.865        13.133        13.513       14.031      14.671 
    coh71:k=35.84,b=0         12.936        13.201        13.578       14.091      14.724 
    coh72:k=36.3456,b=0       13.005        13.269        13.642        14.15      14.778 
    coh73:k=36.8513,b=0       13.074        13.335        13.705       14.208       14.83 
    coh74:k=37.357,b=0        13.142        13.401        13.767       14.266      14.882 
    coh75:k=37.8626,b=0       13.209        13.465        13.829       14.323      14.933 
    coh76:k=38.3683,b=0       13.275        13.529         13.89       14.379      14.984 
    coh77:k=38.874,b=0         13.34        13.593         13.95       14.435      15.034 
    coh78:k=39.3796,b=0       13.405        13.655        14.009       14.489      15.083 
    coh79:k=39.8853,b=0       13.468        13.716        14.067       14.544      15.132 
    coh80:k=40.3909,b=0       13.531        13.777        14.125       14.597       15.18 
    coh81:k=40.8966,b=0       13.593        13.837        14.182        14.65      15.228 
    coh82:k=41.4023,b=0       13.655        13.897        14.239       14.702      15.275 
    coh83:k=41.9079,b=0       13.715        13.955        14.294       14.754      15.322 
    coh84:k=42.4136,b=0       13.775        14.013        14.349       14.805      15.368 
    coh85:k=42.9192,b=0       13.834        14.071        14.404       14.855      15.413 
    coh86:k=43.4249,b=0       13.893        14.127        14.458       14.905      15.458 
    coh87:k=43.9306,b=0       13.951        14.183        14.511       14.955      15.503 
    coh88:k=44.4362,b=0       14.008        14.239        14.563       15.003      15.547 
    coh89:k=44.9419,b=0       14.064        14.293        14.615       15.051      15.591 
    coh90:k=45.4476,b=0        14.12        14.347        14.666       15.099      15.634 
    coh91:k=45.9532,b=0       14.176        14.401        14.717       15.146      15.677 
    coh92:k=46.4589,b=0        14.23        14.453        14.767       15.193      15.719 
    coh93:k=46.9645,b=0       14.284        14.506        14.817       15.239      15.761 
    coh94:k=47.4702,b=0       14.338        14.557        14.866       15.285      15.802 
    coh95:k=47.9759,b=0        14.39        14.608        14.915        15.33      15.843 
    coh96:k=48.4815,b=0       14.443        14.659        14.963       15.375      15.883 
    coh97:k=48.9872,b=0       14.494        14.709         15.01       15.419      15.923 
    coh98:k=49.4929,b=0       14.545        14.758        15.057       15.463      15.963 
    coh99:k=49.9985,b=0       14.596        14.807        15.104       15.506      16.002 
    coh100:k=50.5042,b=0      14.646        14.855         15.15       15.549      16.041 
    coh101:k=51.0098,b=0      14.695        14.903        15.196       15.591      16.079 
    coh102:k=51.5155,b=0      14.744        14.951        15.241       15.633      16.117 
    coh103:k=52.0212,b=0      14.793        14.998        15.285       15.675      16.154 
    coh104:k=52.5268,b=0      14.841        15.044         15.33       15.716       16.19 
    coh105:k=53.0325,b=0      14.888         15.09        15.373       15.757      16.226 
    coh106:k=53.5381,b=0      14.935        15.135        15.417       15.797      16.261 
    coh107:k=54.0438,b=0      14.982        15.181         15.46       15.837      16.294 
    coh108:k=54.5495,b=0      15.028        15.225        15.502       15.876      16.326 
    coh109:k=55.0551,b=0      15.073        15.269        15.544       15.915      16.356 
    coh110:k=55.5608,b=0      15.118        15.313        15.586       15.954      16.383 
    coh111:k=56.0665,b=0      15.163        15.356        15.627       15.991      16.405 
    coh112:k=56.5721,b=0      15.186        15.378        15.648       16.011      16.417 
    coh113:k=57.0778,b=0      15.189        15.382        15.652       16.014      16.421 

tb_pol_a: optimal safe savings choice for each state space point
                            z1_0_33942    z2_0_5596     z3_0_92263    z4_1_5212      z5_2_508 
                            __________    __________    __________    __________    __________

    coh1:k=0.443648,b=0     0.00019723    0.00019723    0.00024642    0.00024642    0.00024642
    coh2:k=0.94931,b=0      0.00052729    0.00052729    0.00052729    0.00052729    0.00052729
    coh3:k=1.45497,b=0      0.00080816    0.00080816    0.00064682    0.00064682    0.00064682
    coh4:k=1.96063,b=0        0.001089      0.001089      0.001089      0.001089      0.001089
    coh5:k=2.4663,b=0         0.074767     0.0013699     0.0013699     0.0013699     0.0013699
    coh6:k=2.97196,b=0         0.26726     0.0019803     0.0019803     0.0016508     0.0016508
    coh7:k=3.47762,b=0          0.5747     0.0023173     0.0023173     0.0019316     0.0019316
    coh8:k=3.98328,b=0         0.90808     0.0026542     0.0026542     0.0026542     0.0022125
    coh9:k=4.48894,b=0          1.2584     0.0029911     0.0029911     0.0029911     0.0029911
    coh10:k=4.99461,b=0         1.5966       0.17314     0.0033281     0.0033281     0.0033281
    coh11:k=5.50027,b=0         2.5282       0.42901      0.003665      0.003665      0.003665
    coh12:k=6.00593,b=0         2.9068        0.7862      0.004002      0.004002      0.004002
    coh13:k=6.51159,b=0         3.3059        1.8651     0.0043389     0.0043389     0.0043389
    coh14:k=7.01725,b=0         3.6505        2.1857      0.005454     0.0046758     0.0046758
    coh15:k=7.52291,b=0         4.0782        2.6013      0.005847      0.005847     0.0050128
    coh16:k=8.02858,b=0          4.502        3.0243       0.14873       0.00624     0.0053497
    coh17:k=8.53424,b=0         4.8893        3.4033       0.48873      0.006633     0.0056866
    coh18:k=9.0399,b=0          5.2899        3.7158        0.9614      0.007026      0.007026
    coh19:k=9.54556,b=0         5.5983         4.149         1.278      0.007419      0.007419
    coh20:k=10.0512,b=0         5.9719        4.5399        1.6708      0.007812      0.007812
    coh21:k=10.5569,b=0         6.4016        4.8976        2.0996      0.008205      0.008205
    coh22:k=11.0625,b=0         6.8383        5.2667        2.4692     0.0085981     0.0085981
    coh23:k=11.5682,b=0         7.1508        5.6513        2.8698     0.0089911     0.0089911
    coh24:k=12.0739,b=0         7.5769        6.0478        3.2943     0.0093841     0.0093841
    coh25:k=12.5795,b=0         7.9751        6.4558         3.668     0.0097771     0.0097771
    coh26:k=13.0852,b=0         8.3252        6.8753        4.0049       0.01017       0.01017
    coh27:k=13.5909,b=0         8.8139        7.3079        4.4936      0.010563      0.010563
    coh28:k=14.0965,b=0           9.16        7.7548        4.8539      0.010956      0.010956
    coh29:k=14.6022,b=0         9.4886        8.1017        5.2082       0.12285      0.011349
    coh30:k=15.1078,b=0         9.8787        8.4438        5.5739       0.37407      0.011742
    coh31:k=15.6135,b=0         10.393        8.9099        5.9511       0.76783      0.012135
    coh32:k=16.1192,b=0         10.729        9.1985        6.3437        1.1925      0.012528
    coh33:k=16.6248,b=0         12.946        9.6432        6.7484        1.4849      0.012921
    coh34:k=17.1305,b=0         13.339        10.047        7.1644        1.8415      0.013314
    coh35:k=17.6362,b=0         13.737        10.384         7.592        2.2875      0.013707
    coh36:k=18.1418,b=0         14.424        10.904        8.0326        2.5761        0.0141
    coh37:k=18.6475,b=0         14.858        13.171        8.4876        3.0868      0.014493
    coh38:k=19.1531,b=0         15.261        13.766        8.8075        3.4965      0.014886
    coh39:k=19.6588,b=0         15.664        14.241        9.1207        3.8303      0.015279
    coh40:k=20.1645,b=0         16.067        14.608        9.5917        4.1755      0.015672
    coh41:k=20.6701,b=0          16.47        15.106        9.8323        4.5361      0.016065
    coh42:k=21.1758,b=0         16.872        15.723        10.272        4.9088      0.016458
    coh43:k=21.6814,b=0         17.326        16.099        10.784         5.293      0.016851
    coh44:k=22.1871,b=0          18.08        16.474        13.665        5.6885      0.017244
    coh45:k=22.6928,b=0         18.492         16.85        13.976        6.0972      0.017637
    coh46:k=23.1984,b=0         18.904        17.225        14.622        6.5202       0.01803
    coh47:k=23.7041,b=0         19.316        17.601        15.028        6.7726      0.018423
    coh48:k=24.2098,b=0         19.728        18.229        15.349        7.0173      0.018816
    coh49:k=24.7154,b=0          20.14        18.799        15.669        10.066        0.6777
    coh50:k=25.2211,b=0         20.552        19.183        16.152        10.677         1.097
    coh64:k=32.3003,b=0         26.905        25.152        22.231        16.972        7.5083
    coh65:k=32.806,b=0          27.326        25.546        22.989        17.649        7.7435
    coh66:k=33.3117,b=0         27.747         26.29        23.529        18.106        8.2132
    coh67:k=33.8173,b=0         28.168        26.945        23.886        18.381        8.5939
    coh68:k=34.323,b=0           28.59        27.348        24.244        18.656        8.9455
    coh69:k=34.8287,b=0         29.011        27.751        24.601        19.087         9.637
    coh70:k=35.3343,b=0         29.432        28.154        24.958        19.845        10.258
    coh71:k=35.84,b=0           29.853        28.557         25.33        20.129         10.42
    coh72:k=36.3456,b=0         30.274         28.96        26.273        20.413        11.152
    coh73:k=36.8513,b=0         30.696        29.362        26.696        21.233        11.365
    coh74:k=37.357,b=0          31.117        29.765        27.062        21.657         11.99
    coh75:k=37.8626,b=0         31.538        30.168        27.429         21.95        12.361
    coh76:k=38.3683,b=0         31.959        30.571        27.795        22.243        12.855
    coh77:k=38.874,b=0           32.38        30.974        28.161         22.79        13.395
    coh78:k=39.3796,b=0          32.98        31.377        28.528        23.541        13.569
    coh79:k=39.8853,b=0         33.944         31.78        28.994        23.844        13.843
    coh80:k=40.3909,b=0         34.375        32.202        29.991        24.146        14.648
    coh81:k=40.8966,b=0         34.805        33.263        30.366        24.448        14.831
    coh82:k=41.4023,b=0         35.235        33.737        30.742        25.354        15.619
    coh83:k=41.9079,b=0         35.666        34.149        31.117        25.811        15.956
    coh84:k=42.4136,b=0         36.096        34.562        31.493        26.122        16.149
    coh85:k=42.9192,b=0         36.526        34.974        31.868        26.434         16.71
    coh86:k=43.4249,b=0         36.957        35.386        32.244        26.745        17.319
    coh87:k=43.9306,b=0         37.387        35.798        32.619        27.057        17.521
    coh88:k=44.4362,b=0         37.817         36.21        32.995        27.481        17.836
    coh89:k=44.9419,b=0         38.248        36.622         33.37        28.492        18.737
    coh90:k=45.4476,b=0         38.678        37.034        33.746        28.813        18.948
    coh91:k=45.9532,b=0         39.108        37.446        34.793        29.134        19.159
    coh92:k=46.4589,b=0         39.539        37.858        35.337        29.454        19.957
    coh93:k=46.9645,b=0         39.969         38.27        35.721        29.775         20.43
    coh94:k=47.4702,b=0         40.399        38.682        36.106        30.505         20.65
    coh95:k=47.9759,b=0          40.83        39.094        36.491        31.284        21.188
    coh96:k=48.4815,b=0          41.26        39.506        36.875        31.613        21.967
    coh97:k=48.9872,b=0          41.69        39.918         37.26        31.943        22.196
    coh98:k=49.4929,b=0         42.121         40.33        37.644        32.273        22.425
    coh99:k=49.9985,b=0         42.551        40.742        38.029        32.603        22.654
    coh100:k=50.5042,b=0        42.981        41.154        38.414        32.932        23.625
    coh101:k=51.0098,b=0        43.412        41.566        38.798        33.262        24.035
    coh102:k=51.5155,b=0        43.842        41.978        39.183        34.142        24.273
    coh103:k=52.0212,b=0        44.272        42.842        39.567        34.863        24.963
    coh104:k=52.5268,b=0        44.703        43.753        40.303        35.201          25.7
    coh105:k=53.0325,b=0        45.133        44.174        41.296         35.54        25.948
    coh106:k=53.5381,b=0        45.563        44.595         41.69        35.879        26.336
    coh107:k=54.0438,b=0        45.994        45.016        42.083        36.218        27.453
    coh108:k=54.5495,b=0        46.424        45.437        42.477        36.557        28.588
    coh109:k=55.0551,b=0        46.854        45.859        42.871        36.896        28.929
    coh110:k=55.5608,b=0        47.285         46.28        43.265        37.942        31.316
    coh111:k=56.0665,b=0        47.715        46.701        43.659        38.588        34.307
    coh112:k=56.5721,b=0        48.156        47.137        44.082         38.99        35.935
    coh113:k=57.0778,b=0        48.605        47.586        44.531        39.439        36.384

tb_pol_k: optimal risky investment choice for each state space point
                            z1_0_33942    z2_0_5596    z3_0_92263    z4_1_5212    z5_2_508
                            __________    _________    __________    _________    ________

    coh1:k=0.443648,b=0      0.19703       0.19703      0.24618       0.24618     0.24618 
    coh2:k=0.94931,b=0       0.52676       0.52676      0.52676       0.52676     0.52676 
    coh3:k=1.45497,b=0       0.80735       0.80735      0.64617       0.64617     0.64617 
    coh4:k=1.96063,b=0        1.0879        1.0879       1.0879        1.0879      1.0879 
    coh5:k=2.4663,b=0         1.5686        1.3685       1.3685        1.3685      1.3685 
    coh6:k=2.97196,b=0        1.7131        1.9783       1.9783        1.6491      1.6491 
    coh7:k=3.47762,b=0        1.7426        2.3149       2.3149        1.9297      1.9297 
    coh8:k=3.98328,b=0        1.7461        2.6515       2.6515        2.6515      2.2103 
    coh9:k=4.48894,b=0        1.7327        2.9881       2.9881        2.9881      2.9881 
    coh10:k=4.99461,b=0       1.7315        3.1549       3.3247        3.3247      3.3247 
    coh11:k=5.50027,b=0       1.7467         3.236       3.6613        3.6613      3.6613 
    coh12:k=6.00593,b=0       1.7612        3.2158       3.9979        3.9979      3.9979 
    coh13:k=6.51159,b=0        1.755        3.1958       4.3346        4.3346      4.3346 
    coh14:k=7.01725,b=0       1.8035        3.2682       5.4485        4.6712      4.6712 
    coh15:k=7.52291,b=0       1.7688        3.2457       5.8411        5.8411      5.0078 
    coh16:k=8.02858,b=0        1.738        3.2156       6.0913        6.2337      5.3444 
    coh17:k=8.53424,b=0       1.7437        3.2297       6.1443        6.6264       5.681 
    coh18:k=9.0399,b=0        1.7361        3.3102       6.0646         7.019       7.019 
    coh19:k=9.54556,b=0       1.8207          3.27        6.141        7.4116      7.4116 
    coh20:k=10.0512,b=0       1.8401        3.2721       6.1412        7.8042      7.8042 
    coh21:k=10.5569,b=0       1.8035        3.3075       6.1054        8.1968      8.1968 
    coh22:k=11.0625,b=0       1.7598        3.3314       6.1288        8.5895      8.5895 
    coh23:k=11.5682,b=0       1.8402        3.3398       6.1212        8.9821      8.9821 
    coh24:k=12.0739,b=0       1.8072        3.3363       6.0897        9.3747      9.3747 
    coh25:k=12.5795,b=0        1.802        3.3213       6.1091        9.7673      9.7673 
    coh26:k=13.0852,b=0       1.8449        3.2948       6.1652         10.16       10.16 
    coh27:k=13.5909,b=0       1.7492        3.2552       6.0695        10.553      10.553 
    coh28:k=14.0965,b=0       1.7961        3.2013       6.1022        10.945      10.945 
    coh29:k=14.6022,b=0       1.8606        3.2475       6.1409        11.226      11.338 
    coh30:k=15.1078,b=0       1.8634        3.2983       6.1682        11.368       11.73 
    coh31:k=15.6135,b=0       1.7423        3.2252       6.1841        11.367      12.123 
    coh32:k=16.1192,b=0       1.7987        3.3297       6.1845        11.336      12.516 
    coh33:k=16.6248,b=0       1.8191         3.278       6.1728        11.436      12.908 
    coh34:k=17.1305,b=0       1.8744        3.2674       6.1498        11.473      13.301 
    coh35:k=17.6362,b=0       1.9256        3.3235       6.1153         11.42      13.694 
    coh36:k=18.1418,b=0       1.6883        3.1958       6.0676        11.524      14.086 
    coh37:k=18.6475,b=0       1.7031        3.3896       6.0057        11.406      14.479 
    coh38:k=19.1531,b=0       1.7493        3.2437       6.0788         11.39      14.871 
    coh39:k=19.6588,b=0       1.7954        3.2178       6.1586        11.449      15.264 
    coh40:k=20.1645,b=0       1.8416        3.3006       6.0805        11.497      15.657 
    coh41:k=20.6701,b=0       1.8878        3.2511        6.233        11.529      16.049 
    coh42:k=21.1758,b=0        1.934        3.0831       6.1861        11.549      16.442 
    coh43:k=21.6814,b=0       1.9296        3.1567       6.0669        11.558      16.834 
    coh44:k=22.1871,b=0        1.625        3.2304       6.0397        11.556      17.227 
    coh45:k=22.6928,b=0       1.6621         3.304       6.1773         11.54       17.62 
    coh46:k=23.1984,b=0       1.6991        3.3776       5.9803         11.51      18.012 
    coh47:k=23.7041,b=0       1.7361        3.4512       6.0238        11.651      18.405 
    coh48:k=24.2098,b=0       1.7732        3.2719       6.1523        11.799      18.798 
    coh49:k=24.7154,b=0       1.8102        3.1514       6.2808        11.884      21.272 
    coh50:k=25.2211,b=0       1.8472        3.2159       6.2472        11.722      21.302 
    coh64:k=32.3003,b=0       1.7815        3.5343       6.4556        11.714      21.178 
    coh65:k=32.806,b=0        1.8094        3.5896       6.1461        11.487      21.392 
    coh66:k=33.3117,b=0       1.8373        3.2946       6.0552        11.478      21.371 
    coh67:k=33.8173,b=0       1.8651        3.0886       6.1471        11.652       21.44 
    coh68:k=34.323,b=0         1.893        3.1347        6.239        11.827      21.537 
    coh69:k=34.8287,b=0       1.9209        3.1809       6.3309        11.845      21.295 
    coh70:k=35.3343,b=0       1.9488        3.2271       6.4228        11.536      21.123 
    coh71:k=35.84,b=0         1.9767        3.2733       6.4995        11.701       21.41 
    coh72:k=36.3456,b=0       2.0046        3.3195        6.006        11.866      21.127 
    coh73:k=36.8513,b=0       2.0325        3.3656        6.032        11.495      21.363 
    coh74:k=37.357,b=0        2.0604        3.4118       6.1147        11.521      21.188 
    coh75:k=37.8626,b=0       2.0883         3.458       6.1975        11.677      21.265 
    coh76:k=38.3683,b=0       2.1161        3.5042       6.2803        11.832      21.221 
    coh77:k=38.874,b=0         2.144        3.5504       6.3631        11.734       21.13 
    coh78:k=39.3796,b=0       1.9937        3.5966       6.4458        11.432      21.404 
    coh79:k=39.8853,b=0       1.4783        3.6427       6.4288        11.579       21.58 
    coh80:k=40.3909,b=0       1.4971        3.6698       5.8808        11.726      21.224 
    coh81:k=40.8966,b=0       1.5158        3.0574       5.9544        11.872      21.489 
    coh82:k=41.4023,b=0       1.5346        3.0324        6.028        11.415      21.151 
    coh83:k=41.9079,b=0       1.5533        3.0694       6.1016        11.408      21.263 
    coh84:k=42.4136,b=0       1.5721        3.1065       6.1752        11.546      21.519 
    coh85:k=42.9192,b=0       1.5908        3.1435       6.2489        11.683      21.407 
    coh86:k=43.4249,b=0       1.6095        3.1805       6.3225        11.821      21.247 
    coh87:k=43.9306,b=0       1.6283        3.2176       6.3961        11.959      21.494 
    coh88:k=44.4362,b=0        1.647        3.2546       6.4697        11.983      21.628 
    coh89:k=44.9419,b=0       1.6658        3.2916       6.5434        11.421      21.176 
    coh90:k=45.4476,b=0       1.6845        3.3287        6.617        11.549      21.414 
    coh91:k=45.9532,b=0       1.7033        3.3657       6.0183        11.678      21.653 
    coh92:k=46.4589,b=0        1.722        3.4027       5.9239        11.806      21.304 
    coh93:k=46.9645,b=0       1.7407        3.4398       5.9883        11.935       21.28 
    coh94:k=47.4702,b=0       1.7595        3.4768       6.0528        11.653      21.509 
    coh95:k=47.9759,b=0       1.7782        3.5138       6.1173        11.324       21.42 
    coh96:k=48.4815,b=0        1.797        3.5509       6.1818        11.443       21.09 
    coh97:k=48.9872,b=0       1.8157        3.5879       6.2462        11.563       21.31 
    coh98:k=49.4929,b=0       1.8345         3.625       6.3107        11.682       21.53 
    coh99:k=49.9985,b=0       1.8532         3.662       6.3752        11.802       21.75 
    coh100:k=50.5042,b=0      1.8719         3.699       6.4397        11.921      21.229 
    coh101:k=51.0098,b=0      1.8907        3.7361       6.5041         12.04      21.267 
    coh102:k=51.5155,b=0      1.9094        3.7731       6.5686        11.609      21.478 
    coh103:k=52.0212,b=0      1.9282        3.3586       6.6331        11.338      21.237 
    coh104:k=52.5268,b=0      1.9469         2.897       6.3471        11.448       20.95 
    coh105:k=53.0325,b=0      1.9657        2.9249       5.8028        11.558      21.151 
    coh106:k=53.5381,b=0      1.9844        2.9528       5.8581        11.669      21.211 
    coh107:k=54.0438,b=0      2.0031        2.9807       5.9134        11.779      20.544 
    coh108:k=54.5495,b=0      2.0219        3.0086       5.9687        11.889      19.858 
    coh109:k=55.0551,b=0      2.0406        3.0365       6.0241        11.999      19.966 
    coh110:k=55.5608,b=0      2.0594        3.0644       6.0794        11.402      18.028 
    coh111:k=56.0665,b=0      2.0781        3.0923       6.1347        11.206      15.486 
    coh112:k=56.5721,b=0      2.0867        3.1051       6.1602        11.252      14.307 
    coh113:k=57.0778,b=0      2.0867        3.1051       6.1602        11.252      14.307 

tb_pol_w: risky + safe investment choices (first stage choice, choose within risky vs safe)
                            z1_0_33942    z2_0_5596    z3_0_92263    z4_1_5212    z5_2_508
                            __________    _________    __________    _________    ________

    coh1:k=0.443648,b=0      0.19723       0.19723      0.24642       0.24642     0.24642 
    coh2:k=0.94931,b=0       0.52729       0.52729      0.52729       0.52729     0.52729 
    coh3:k=1.45497,b=0       0.80816       0.80816      0.64682       0.64682     0.64682 
    coh4:k=1.96063,b=0         1.089         1.089        1.089         1.089       1.089 
    coh5:k=2.4663,b=0         1.6434        1.3699       1.3699        1.3699      1.3699 
    coh6:k=2.97196,b=0        1.9803        1.9803       1.9803        1.6508      1.6508 
    coh7:k=3.47762,b=0        2.3173        2.3173       2.3173        1.9316      1.9316 
    coh8:k=3.98328,b=0        2.6542        2.6542       2.6542        2.6542      2.2125 
    coh9:k=4.48894,b=0        2.9911        2.9911       2.9911        2.9911      2.9911 
    coh10:k=4.99461,b=0       3.3281        3.3281       3.3281        3.3281      3.3281 
    coh11:k=5.50027,b=0       4.2749         3.665        3.665         3.665       3.665 
    coh12:k=6.00593,b=0       4.6679         4.002        4.002         4.002       4.002 
    coh13:k=6.51159,b=0        5.061         5.061       4.3389        4.3389      4.3389 
    coh14:k=7.01725,b=0        5.454         5.454        5.454        4.6758      4.6758 
    coh15:k=7.52291,b=0        5.847         5.847        5.847         5.847      5.0128 
    coh16:k=8.02858,b=0         6.24          6.24         6.24          6.24      5.3497 
    coh17:k=8.53424,b=0        6.633         6.633        6.633         6.633      5.6866 
    coh18:k=9.0399,b=0         7.026         7.026        7.026         7.026       7.026 
    coh19:k=9.54556,b=0        7.419         7.419        7.419         7.419       7.419 
    coh20:k=10.0512,b=0        7.812         7.812        7.812         7.812       7.812 
    coh21:k=10.5569,b=0        8.205         8.205        8.205         8.205       8.205 
    coh22:k=11.0625,b=0       8.5981        8.5981       8.5981        8.5981      8.5981 
    coh23:k=11.5682,b=0       8.9911        8.9911       8.9911        8.9911      8.9911 
    coh24:k=12.0739,b=0       9.3841        9.3841       9.3841        9.3841      9.3841 
    coh25:k=12.5795,b=0       9.7771        9.7771       9.7771        9.7771      9.7771 
    coh26:k=13.0852,b=0        10.17         10.17        10.17         10.17       10.17 
    coh27:k=13.5909,b=0       10.563        10.563       10.563        10.563      10.563 
    coh28:k=14.0965,b=0       10.956        10.956       10.956        10.956      10.956 
    coh29:k=14.6022,b=0       11.349        11.349       11.349        11.349      11.349 
    coh30:k=15.1078,b=0       11.742        11.742       11.742        11.742      11.742 
    coh31:k=15.6135,b=0       12.135        12.135       12.135        12.135      12.135 
    coh32:k=16.1192,b=0       12.528        12.528       12.528        12.528      12.528 
    coh33:k=16.6248,b=0       14.765        12.921       12.921        12.921      12.921 
    coh34:k=17.1305,b=0       15.214        13.314       13.314        13.314      13.314 
    coh35:k=17.6362,b=0       15.663        13.707       13.707        13.707      13.707 
    coh36:k=18.1418,b=0       16.112          14.1         14.1          14.1        14.1 
    coh37:k=18.6475,b=0       16.561        16.561       14.493        14.493      14.493 
    coh38:k=19.1531,b=0        17.01         17.01       14.886        14.886      14.886 
    coh39:k=19.6588,b=0       17.459        17.459       15.279        15.279      15.279 
    coh40:k=20.1645,b=0       17.908        17.908       15.672        15.672      15.672 
    coh41:k=20.6701,b=0       18.357        18.357       16.065        16.065      16.065 
    coh42:k=21.1758,b=0       18.806        18.806       16.458        16.458      16.458 
    coh43:k=21.6814,b=0       19.256        19.256       16.851        16.851      16.851 
    coh44:k=22.1871,b=0       19.705        19.705       19.705        17.244      17.244 
    coh45:k=22.6928,b=0       20.154        20.154       20.154        17.637      17.637 
    coh46:k=23.1984,b=0       20.603        20.603       20.603         18.03       18.03 
    coh47:k=23.7041,b=0       21.052        21.052       21.052        18.423      18.423 
    coh48:k=24.2098,b=0       21.501        21.501       21.501        18.816      18.816 
    coh49:k=24.7154,b=0        21.95         21.95        21.95         21.95       21.95 
    coh50:k=25.2211,b=0       22.399        22.399       22.399        22.399      22.399 
    coh64:k=32.3003,b=0       28.686        28.686       28.686        28.686      28.686 
    coh65:k=32.806,b=0        29.135        29.135       29.135        29.135      29.135 
    coh66:k=33.3117,b=0       29.584        29.584       29.584        29.584      29.584 
    coh67:k=33.8173,b=0       30.034        30.034       30.034        30.034      30.034 
    coh68:k=34.323,b=0        30.483        30.483       30.483        30.483      30.483 
    coh69:k=34.8287,b=0       30.932        30.932       30.932        30.932      30.932 
    coh70:k=35.3343,b=0       31.381        31.381       31.381        31.381      31.381 
    coh71:k=35.84,b=0          31.83         31.83        31.83         31.83       31.83 
    coh72:k=36.3456,b=0       32.279        32.279       32.279        32.279      32.279 
    coh73:k=36.8513,b=0       32.728        32.728       32.728        32.728      32.728 
    coh74:k=37.357,b=0        33.177        33.177       33.177        33.177      33.177 
    coh75:k=37.8626,b=0       33.626        33.626       33.626        33.626      33.626 
    coh76:k=38.3683,b=0       34.075        34.075       34.075        34.075      34.075 
    coh77:k=38.874,b=0        34.524        34.524       34.524        34.524      34.524 
    coh78:k=39.3796,b=0       34.973        34.973       34.973        34.973      34.973 
    coh79:k=39.8853,b=0       35.423        35.423       35.423        35.423      35.423 
    coh80:k=40.3909,b=0       35.872        35.872       35.872        35.872      35.872 
    coh81:k=40.8966,b=0       36.321        36.321       36.321        36.321      36.321 
    coh82:k=41.4023,b=0        36.77         36.77        36.77         36.77       36.77 
    coh83:k=41.9079,b=0       37.219        37.219       37.219        37.219      37.219 
    coh84:k=42.4136,b=0       37.668        37.668       37.668        37.668      37.668 
    coh85:k=42.9192,b=0       38.117        38.117       38.117        38.117      38.117 
    coh86:k=43.4249,b=0       38.566        38.566       38.566        38.566      38.566 
    coh87:k=43.9306,b=0       39.015        39.015       39.015        39.015      39.015 
    coh88:k=44.4362,b=0       39.464        39.464       39.464        39.464      39.464 
    coh89:k=44.9419,b=0       39.913        39.913       39.913        39.913      39.913 
    coh90:k=45.4476,b=0       40.362        40.362       40.362        40.362      40.362 
    coh91:k=45.9532,b=0       40.812        40.812       40.812        40.812      40.812 
    coh92:k=46.4589,b=0       41.261        41.261       41.261        41.261      41.261 
    coh93:k=46.9645,b=0        41.71         41.71        41.71         41.71       41.71 
    coh94:k=47.4702,b=0       42.159        42.159       42.159        42.159      42.159 
    coh95:k=47.9759,b=0       42.608        42.608       42.608        42.608      42.608 
    coh96:k=48.4815,b=0       43.057        43.057       43.057        43.057      43.057 
    coh97:k=48.9872,b=0       43.506        43.506       43.506        43.506      43.506 
    coh98:k=49.4929,b=0       43.955        43.955       43.955        43.955      43.955 
    coh99:k=49.9985,b=0       44.404        44.404       44.404        44.404      44.404 
    coh100:k=50.5042,b=0      44.853        44.853       44.853        44.853      44.853 
    coh101:k=51.0098,b=0      45.302        45.302       45.302        45.302      45.302 
    coh102:k=51.5155,b=0      45.751        45.751       45.751        45.751      45.751 
    coh103:k=52.0212,b=0      46.201        46.201       46.201        46.201      46.201 
    coh104:k=52.5268,b=0       46.65         46.65        46.65         46.65       46.65 
    coh105:k=53.0325,b=0      47.099        47.099       47.099        47.099      47.099 
    coh106:k=53.5381,b=0      47.548        47.548       47.548        47.548      47.548 
    coh107:k=54.0438,b=0      47.997        47.997       47.997        47.997      47.997 
    coh108:k=54.5495,b=0      48.446        48.446       48.446        48.446      48.446 
    coh109:k=55.0551,b=0      48.895        48.895       48.895        48.895      48.895 
    coh110:k=55.5608,b=0      49.344        49.344       49.344        49.344      49.344 
    coh111:k=56.0665,b=0      49.793        49.793       49.793        49.793      49.793 
    coh112:k=56.5721,b=0      50.242        50.242       50.242        50.242      50.242 
    coh113:k=57.0778,b=0      50.691        50.691       50.691        50.691      50.691 

end
ans = 

  Map with properties:

        Count: 15
      KeyType: char
    ValueType: any