Solve Save + Borr Dynamic Programming Problem (Loop)
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Contents
- FF_ABZ_VF solve infinite horizon exo shock + endo asset problem
- Default
- Parse Parameters 1
- Parse Parameters 2
- Display Parameters
- Initialize Output Matrixes
- Initialize Convergence Conditions
- Iterate Value Function
- Iterate over a and z states
- Store Optimal Choices and Value Given(a,z)
- Check Tolerance and Continuation
- Process Optimal Choices
function result_map = ff_abz_vf(varargin)
FF_ABZ_VF solve infinite horizon exo shock + endo asset problem
This program solves the infinite horizon dynamic single asset and single shock problem with loops. This file contains codes that processes borrowing.
The borrowing problem is very similar to the savings problem. The code could be identical if one does not have to deal with default. The main addition here in comparison to the savings only code ff_az_vf is the ability to deal with default.
@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:
- mt_val matrix states_n by shock_n matrix of converged value function grid
- mt_pol_a matrix states_n by shock_n matrix of converged policy function grid
- ar_val_diff_norm array if bl_post = true it_iter_last by 1 val function difference between iteration
- ar_pol_diff_norm array if bl_post = true it_iter_last by 1 policy function difference between iterations
- mt_pol_perc_change matrix if bl_post = true it_iter_last by shock_n the proportion of grid points at which policy function changed between current and last iteration for each element of shock
@example
% Get Default Parameters
it_param_set = 2;
[param_map, support_map] = ffs_abz_set_default_param(it_param_set);
% Chnage param_map keys for borrowing
param_map('fl_b_bd') = -20; % borrow bound
param_map('bl_default') = false; % true if allow for default
param_map('fl_c_min') = 0.0001; % u(c_min) when default
% Change Keys in param_map
param_map('it_a_n') = 500;
param_map('fl_z_r_borr_n') = 5;
param_map('it_z_wage_n') = 15;
param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');
param_map('fl_a_max') = 100;
param_map('fl_w') = 1.3;
% Change Keys support_map
support_map('bl_display') = false;
support_map('bl_post') = true;
support_map('bl_display_final') = false;
% Call Program with external parameters that override defaults.
ff_abz_vf(param_map, support_map);@include
@seealso
- save loop: ff_az_vf
- save vectorized: ff_az_vf_vec
- save optimized-vectorized: ff_az_vf_vecsv
- save + borr loop: ff_abz_vf
- save + borr vectorized: ff_abz_vf_vec
- save + borr optimized-vectorized: ff_abz_vf_vecsv
Default
- it_param_set = 1: quick test
- it_param_set = 2: benchmark run
- it_param_set = 3: benchmark profile
- it_param_set = 4: press publish button
it_param_set = 4; bl_input_override = true; [param_map, support_map] = ffs_abz_set_default_param(it_param_set); % Note: param_map and support_map can be adjusted here or outside to override defaults param_map('it_a_n') = 75; param_map('fl_z_r_borr_n') = 3; param_map('it_z_wage_n') = 5; param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n'); % param_map('fl_r_save') = 0.025; % param_map('fl_r_borr') = 0.035; [armt_map, func_map] = ffs_abz_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_abz_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_abz_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_a', 'mt_z_trans', 'ar_z_r_borr_mesh_wage', 'ar_z_wage_mesh_r_borr'}); [ar_a, mt_z_trans, ar_z_r_borr_mesh_wage, ar_z_wage_mesh_r_borr] = params_group{:}; % func_map params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons_checkcmin', 'f_awithr_to_anor', 'f_coh', 'f_cons_coh'}); [f_util_log, f_util_crra, f_cons_checkcmin, f_awithr_to_anor, f_coh, f_cons_coh] = params_group{:}; % param_map params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min',... 'fl_nan_replace', 'bl_default', 'fl_default_aprime'}); [it_a_n, it_z_n, fl_crra, fl_beta, fl_c_min, ... fl_nan_replace, bl_default, fl_default_aprime] = 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_display_defparam', '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_display_defparam, bl_display, it_display_every, bl_post] = params_group{:};
Display Parameters
if(bl_display_defparam) fft_container_map_display(param_map); fft_container_map_display(support_map); end
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
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Map with properties:
Count: 35
KeyType: char
ValueType: any
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pos = 32 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 33 ; key = st_model ; val = abz
pos = 34 ; key = st_z_r_borr_drv_ele_type ; val = unif
pos = 35 ; key = st_z_r_borr_drv_prb_type ; val = poiss
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Scalars in Container and Sizes and Basic Statistics
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i idx value
__ ___ ______
bl_b_is_principle 1 1 1
bl_default 2 2 1
bl_loglin 3 3 0
fl_a_max 4 4 50
fl_a_min 5 5 0
fl_b_bd 6 6 -20
fl_beta 7 7 0.94
fl_c_min 8 8 0.01
fl_crra 9 9 1.5
fl_default_aprime 10 10 0
fl_loglin_threshold 11 11 1
fl_nan_replace 12 12 -99999
fl_r_save 13 13 0.025
fl_tol_dist 14 14 1e-05
fl_tol_pol 15 15 1e-05
fl_tol_val 16 16 1e-05
fl_w 17 17 1.28
fl_z_r_borr_max 18 18 0.095
fl_z_r_borr_min 19 19 0.025
fl_z_r_borr_n 20 20 3
fl_z_r_borr_poiss_mean 21 21 10
fl_z_wage_mu 22 22 0
fl_z_wage_rho 23 23 0.8
fl_z_wage_sig 24 24 0.2
it_a_n 25 25 75
it_maxiter_dist 26 26 1000
it_maxiter_val 27 27 1000
it_tol_pol_nochange 28 28 25
it_trans_power_dist 29 29 1000
it_z_n 30 30 15
it_z_wage_n 31 31 5
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Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
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Map with properties:
Count: 40
KeyType: char
ValueType: any
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pos = 26 ; key = st_img_name_main ; val = ff_abz_vf_default
pos = 27 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_abz//solve/img/
pos = 28 ; key = st_img_prefix ; val =
pos = 29 ; key = st_img_suffix ; val = _p4.png
pos = 30 ; key = st_mat_name_main ; val = ff_abz_vf_default
pos = 31 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_abz//solve/mat/
pos = 32 ; key = st_mat_prefix ; val =
pos = 33 ; key = st_mat_suffix ; val = _p4
pos = 34 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_abz//test/ff_az_ds_vecsv/mat/
pos = 35 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_abz/
pos = 36 ; key = st_profile_name_main ; val = ff_abz_vf_default
pos = 37 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_abz//solve/profile/
pos = 38 ; key = st_profile_prefix ; val =
pos = 39 ; key = st_profile_suffix ; val = _p4
pos = 40 ; key = st_title_prefix ; val =
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Scalars in Container and Sizes and Basic Statistics
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i idx value
__ ___ _____
bl_display 1 1 0
bl_display_defparam 2 2 1
bl_display_dist 3 3 0
bl_display_final 4 4 1
bl_display_final_dist 5 5 0
bl_display_final_dist_detail 6 6 0
bl_display_funcgrids 7 7 0
bl_graph 8 8 1
bl_graph_coh_t_coh 9 9 1
bl_graph_funcgrids 10 10 0
bl_graph_onebyones 11 11 1
bl_graph_pol_lvl 12 12 1
bl_graph_pol_pct 13 13 1
bl_graph_val 14 14 1
bl_img_save 15 15 0
bl_mat 16 16 0
bl_post 17 17 1
bl_profile 18 18 0
bl_profile_dist 19 19 0
bl_time 20 20 1
it_display_every 21 21 5
it_display_final_colmax 22 22 15
it_display_final_rowmax 23 23 100
it_display_summmat_colmax 24 24 5
it_display_summmat_rowmax 25 25 5
Initialize Output Matrixes
mt_val_cur = zeros(length(ar_a),it_z_n); mt_val = mt_val_cur - 1; mt_pol_a = zeros(length(ar_a),it_z_n); mt_pol_a_cur = mt_pol_a - 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]);
Iterate Value Function
Loop solution with 4 nested loops
- loop 1: over exogenous states
- loop 2: over endogenous states
- loop 3: over choices
- 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 % Utility at-Default/at-limiting-case-when-nodefault if (fl_crra == 1) fl_u_cmin = f_util_log(fl_c_min); else fl_u_cmin = f_util_crra(fl_c_min); end % Value Function Iteration while bl_vfi_continue
it_iter = it_iter + 1;
Iterate over a and z states
Solve Problem if Default: coh < borr_bound, then: u(c_min) + EV(a'=0,z') these are the values for defaulter if do not borrow enough to pay debt: a'=0 if save more than what you have: a'=0 if borrowing, possible that all ar_val_cur values are u(cmin), when that is the case, utility equal to c_min, this means given current choice set, can only default, get utility at c_min level, and a' go to 0. See maximization over loop 3 choices for loop 1+2 states. see README_cminymin_borrsave for additional discussions.
when default is not allowed, there should be exactly one element of the state space where we enter this condition. That is at a_min and z_min. At this point, the natural borrowing constraint when fully used up leads to c = 0. When default is not allowed, this is the limiting case. We solve the limiting case as if default is possible. see the figure here: ffs_abz_get_funcgrid_nodefault. For the figure under section Generate Borrowing A Grid with Default, there are no points to the lower right of the red horizontal and verticle lines, because no default is allowed. But the intersection of the two red lines is this limiting case where c = 0.
when default is allowed. See again ffs_abz_get_funcgrid_nodefault. Again under section Generate Borrowing A Grid with Default, see that there is an area to the right bottom of the two blue horizontal and vertical lines. For all points in that area, the household has to default, they can not borrow even at max to get positive consumption. At other points higher than the blue horizontal line, it is also possible for defaulting to be the optimal choice.
% loop 1: over exogenous states for it_z_i = 1:it_z_n % Current Shock fl_z_r_borr = ar_z_r_borr_mesh_wage(it_z_i); fl_z_wage = ar_z_wage_mesh_r_borr(it_z_i); % loop 2: over endogenous states for it_a_j = 1:length(ar_a)
fl_a = ar_a(it_a_j);
ar_val_cur = zeros(size(ar_a));
% calculate cash on hand
fl_coh = f_coh(fl_z_wage, fl_a);
% loop 3: over choices
for it_ap_k = 1:length(ar_a)
% get next period asset choice
fl_ap = ar_a(it_ap_k);
% calculate consumption
fl_c = f_cons_coh(fl_coh, fl_z_r_borr, fl_ap);
% assign u(c)
if (fl_c <= fl_c_min)
if (bl_default)
% defaults
% current utility: only today u(cmin)
ar_val_cur(it_ap_k) = fl_u_cmin;
% transition out next period, debt wiped out
for it_az_q = 1:it_z_n
ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ...
fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur((ar_a == fl_default_aprime), it_az_q);
end
else
% if default is not allowed: v = fl_nan_replace
ar_val_cur(it_ap_k) = fl_nan_replace;
end
else
% Solve Optimization Problem: max_{a'} u(c(a,a',z)) + beta*EV(a',z')
% borrowed enough to pay debt (and borrowing limit not exceeded)
% saved only the coh available.
% current utility
if (fl_crra == 1)
ar_val_cur(it_ap_k) = f_util_log(fl_c);
else
ar_val_cur(it_ap_k) = f_util_crra(fl_c);
end
% loop 4: add future utility, integration--loop over future shocks
for it_az_q = 1:it_z_n
ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ...
fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur(it_ap_k, it_az_q);
end
end
end
% optimal choice value
[fl_opti_val_z, fl_opti_idx_z] = max(ar_val_cur);
fl_opti_aprime_z = ar_a(fl_opti_idx_z);
fl_opti_c_z = f_cons_coh(fl_coh, fl_z_r_borr, fl_opti_aprime_z);
% Handle Default is optimal or not
if (fl_opti_c_z <= fl_c_min)
if (bl_default)
% if defaulting is optimal choice, at these states, not required
% to default, non-default possible, but default could be optimal
fl_opti_aprime_z = fl_default_aprime;
else
% if default is not allowed, then next period same state as now
% this is absorbing state, this is the limiting case, single
% state space point, lowest a and lowest shock has this.
fl_opti_aprime_z = fl_a;
end
end
Store Optimal Choices and Value Given(a,z)
mt_val(it_a_j,it_z_i) = fl_opti_val_z;
mt_pol_a(it_a_j,it_z_i) = fl_opti_aprime_z;
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); mt_pol_perc_change(it_iter, :) = sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n); % Update mt_val_cur = mt_val; mt_pol_a_cur = mt_pol_a; % 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); ... mt_val_cur(it_a_n,:); mt_pol_a_cur(it_a_n,:)]); tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2)))); tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'Hval', 'Hap'}; disp('mval = mean(mt_val_cur,1), average value over a') disp('map = mean(mt_pol_a_cur,1), average choice over a') disp('Hval = mt_val_cur(it_a_n,:), highest a state val') disp('Hap = mt_pol_a_cur(it_a_n,:), highest a 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
Elapsed time is 612.536238 seconds.
Process Optimal Choices
result_map = containers.Map('KeyType','char', 'ValueType','any'); result_map('mt_val') = mt_val; result_map('cl_mt_val') = {mt_val, zeros(1)}; result_map('cl_mt_coh') = {f_coh(ar_z_wage_mesh_r_borr, ar_a'), zeros(1)}; result_map('cl_mt_pol_a') = {f_awithr_to_anor(ar_z_r_borr_mesh_wage, mt_pol_a), zeros(1)}; result_map('cl_mt_pol_c') = {f_cons_checkcmin(ar_z_r_borr_mesh_wage, ar_z_wage_mesh_r_borr, ar_a', mt_pol_a), zeros(1)}; result_map('ar_st_pol_names') = ["cl_mt_val", "cl_mt_pol_a", "cl_mt_coh", "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, :); result_map = ff_az_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))/(it_a_n): percentage of state space points conditional on shock where the policy function is changing across iterations
valgap polgap zi1_zr_0_025_zw_0_33942 zi2_zr_0_025_zw_0_5596 zi3_zr_0_025_zw_0_92263 zi4_zr_0_025_zw_1_5212 zi5_zr_0_025_zw_2_508 zi6_zr_0_06_zw_0_33942 zi7_zr_0_06_zw_0_5596 zi8_zr_0_06_zw_0_92263 zi9_zr_0_06_zw_1_5212 zi10_zr_0_06_zw_2_508 zi11_zr_0_095_zw_0_33942 zi12_zr_0_095_zw_0_5596 zi13_zr_0_095_zw_0_92263 zi14_zr_0_095_zw_1_5212 zi15_zr_0_095_zw_2_508
________ ______ _______________________ ______________________ _______________________ ______________________ _____________________ ______________________ _____________________ ______________________ _____________________ _____________________ ________________________ _______________________ ________________________ _______________________ ______________________
iter=1 65.172 633.35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
iter=2 55.481 697.53 0.98667 1 0.98667 1 1 0.98667 0.98667 1 0.98667 1 0.97333 0.96 0.97333 0.98667 1
iter=3 42.718 222.16 0.96 0.97333 0.96 0.97333 1 0.97333 0.96 0.98667 0.97333 0.97333 0.94667 0.97333 0.96 0.96 0.98667
iter=4 34.252 114.2 0.92 0.94667 0.93333 0.94667 0.96 0.92 0.92 0.93333 0.93333 0.96 0.90667 0.94667 0.92 0.94667 0.96
iter=5 28.491 65.961 0.86667 0.88 0.84 0.88 0.89333 0.85333 0.85333 0.88 0.88 0.90667 0.86667 0.88 0.85333 0.88 0.92
iter=6 24.283 45.62 0.82667 0.77333 0.77333 0.81333 0.85333 0.82667 0.77333 0.78667 0.81333 0.86667 0.8 0.77333 0.76 0.82667 0.82667
iter=7 20.984 33.283 0.72 0.70667 0.70667 0.72 0.78667 0.72 0.74667 0.70667 0.69333 0.77333 0.74667 0.72 0.72 0.72 0.76
iter=8 18.295 24.642 0.61333 0.62667 0.6 0.64 0.65333 0.6 0.6 0.62667 0.61333 0.69333 0.6 0.61333 0.6 0.61333 0.66667
iter=9 16.057 22.22 0.44 0.49333 0.48 0.50667 0.56 0.44 0.48 0.49333 0.49333 0.56 0.45333 0.48 0.48 0.50667 0.54667
iter=10 14.16 16.068 0.36 0.42667 0.42667 0.41333 0.45333 0.38667 0.41333 0.4 0.38667 0.48 0.38667 0.41333 0.4 0.41333 0.45333
iter=11 12.527 12.742 0.28 0.28 0.29333 0.32 0.37333 0.30667 0.26667 0.30667 0.33333 0.38667 0.29333 0.28 0.30667 0.34667 0.38667
iter=12 11.082 11.61 0.25333 0.26667 0.26667 0.26667 0.29333 0.24 0.24 0.28 0.22667 0.29333 0.24 0.24 0.28 0.22667 0.26667
iter=13 9.7712 10.41 0.22667 0.21333 0.22667 0.24 0.24 0.22667 0.2 0.21333 0.22667 0.25333 0.22667 0.21333 0.21333 0.22667 0.22667
iter=14 8.6441 9.1353 0.18667 0.21333 0.2 0.17333 0.22667 0.13333 0.21333 0.21333 0.17333 0.22667 0.14667 0.18667 0.22667 0.16 0.21333
iter=15 7.6535 9.3668 0.18667 0.13333 0.16 0.18667 0.18667 0.17333 0.14667 0.18667 0.18667 0.2 0.17333 0.13333 0.18667 0.18667 0.17333
iter=16 6.7818 7.5957 0.12 0.13333 0.16 0.13333 0.17333 0.093333 0.13333 0.14667 0.14667 0.18667 0.093333 0.10667 0.14667 0.12 0.16
iter=17 6.0432 7.3872 0.12 0.10667 0.12 0.13333 0.12 0.10667 0.13333 0.12 0.12 0.12 0.10667 0.10667 0.13333 0.10667 0.12
iter=18 5.4139 7.8713 0.093333 0.14667 0.093333 0.10667 0.14667 0.093333 0.14667 0.08 0.12 0.16 0.10667 0.13333 0.08 0.12 0.14667
iter=19 4.8819 6.9847 0.10667 0.08 0.08 0.10667 0.08 0.10667 0.093333 0.08 0.12 0.093333 0.12 0.066667 0.08 0.093333 0.12
iter=20 4.4358 6.0895 0.053333 0.08 0.066667 0.10667 0.093333 0.053333 0.093333 0.066667 0.093333 0.093333 0.053333 0.093333 0.08 0.093333 0.10667
iter=21 4.038 4.3313 0.026667 0.08 0.093333 0.053333 0.053333 0.04 0.08 0.093333 0.066667 0.053333 0.04 0.066667 0.093333 0.04 0.066667
iter=22 3.676 5.8123 0.093333 0.053333 0.066667 0.066667 0.093333 0.066667 0.066667 0.08 0.066667 0.10667 0.08 0.053333 0.066667 0.10667 0.093333
iter=23 3.35 4.5998 0.04 0.053333 0.093333 0.053333 0.066667 0.053333 0.04 0.093333 0.066667 0.066667 0.04 0.04 0.093333 0.066667 0.08
iter=24 3.0579 4.0683 0.04 0.053333 0.04 0.04 0.053333 0.04 0.053333 0.04 0.04 0.053333 0.04 0.053333 0.04 0.04 0.053333
iter=25 2.8022 4.4267 0.04 0.053333 0.026667 0.053333 0.053333 0.053333 0.053333 0.026667 0.053333 0.066667 0.04 0.066667 0.026667 0.053333 0.053333
iter=26 2.5729 3.5821 0.04 0.04 0.026667 0.04 0.053333 0.04 0.053333 0.026667 0.04 0.053333 0.04 0.04 0.04 0.053333 0.053333
iter=27 2.3659 3.3645 0.04 0.04 0.026667 0.04 0.053333 0.04 0.04 0.026667 0.04 0.04 0.04 0.04 0.026667 0.04 0.053333
iter=28 2.1864 3.4895 0.026667 0 0.04 0.053333 0.013333 0.026667 0 0.04 0.053333 0.013333 0.026667 0.013333 0.04 0.053333 0.013333
iter=29 2.0277 2.9335 0.04 0.026667 0.026667 0.013333 0.026667 0.04 0.026667 0.026667 0.013333 0.026667 0.053333 0.026667 0.026667 0.013333 0.026667
iter=30 1.8867 2.3488 0.013333 0.013333 0.026667 0.026667 0.026667 0.013333 0.013333 0.026667 0.026667 0.026667 0.013333 0.013333 0.026667 0.026667 0.026667
iter=31 1.7625 2.3488 0.026667 0.026667 0.026667 0.013333 0.013333 0.026667 0.026667 0.026667 0.013333 0.013333 0.026667 0.026667 0.026667 0.013333 0.013333
iter=32 1.6519 2.3488 0 0.013333 0.013333 0.013333 0.026667 0 0.013333 0.013333 0.013333 0.026667 0 0.013333 0.013333 0.013333 0.026667
iter=33 1.5532 2.8767 0.013333 0.013333 0.04 0.013333 0.026667 0.013333 0.013333 0.04 0.013333 0.026667 0.013333 0.013333 0.04 0.013333 0.026667
iter=34 1.4635 2.3488 0.026667 0.013333 0.026667 0.026667 0.013333 0.026667 0.013333 0.026667 0.026667 0.013333 0.026667 0.013333 0.026667 0.026667 0.013333
iter=35 1.3818 2.6873 0 0.026667 0.013333 0.013333 0.013333 0 0.026667 0.013333 0.013333 0.013333 0 0.026667 0.013333 0.013333 0.013333
iter=36 1.3067 1.6609 0.013333 0.013333 0.013333 0 0.013333 0.013333 0.013333 0.013333 0 0.013333 0.013333 0.013333 0.013333 0 0.013333
iter=37 1.2375 2.3488 0.013333 0 0.013333 0.026667 0.026667 0.013333 0 0.013333 0.026667 0.026667 0.013333 0 0.013333 0.026667 0.026667
iter=38 1.1731 2.3488 0 0.026667 0.026667 0.013333 0 0 0.026667 0.026667 0.013333 0 0 0.026667 0.026667 0.013333 0
iter=39 1.1133 2.3488 0.013333 0 0 0 0.026667 0.013333 0 0 0 0.026667 0.013333 0 0 0 0.026667
iter=40 1.0572 2.3488 0 0.026667 0.026667 0.013333 0.013333 0 0.013333 0.026667 0.013333 0.013333 0 0.013333 0.026667 0.013333 0.013333
iter=41 1.0048 2.3488 0.013333 0 0.013333 0.026667 0 0.013333 0 0.013333 0.026667 0 0.013333 0 0.013333 0.026667 0
iter=42 0.95538 2.3488 0.013333 0.013333 0.013333 0 0.026667 0.013333 0.013333 0.013333 0 0.026667 0.013333 0.013333 0.013333 0 0.026667
iter=43 0.90874 2.3488 0.013333 0.026667 0 0.013333 0 0.013333 0.026667 0 0.013333 0 0.013333 0.026667 0 0.013333 0
iter=44 0.86469 1.6609 0 0 0.013333 0 0.013333 0 0 0.013333 0 0.013333 0 0 0.013333 0 0.013333
iter=45 0.82291 1.6609 0.013333 0.013333 0 0.013333 0.013333 0.013333 0.013333 0 0.013333 0.013333 0.013333 0.013333 0 0.013333 0.013333
iter=46 0.78326 1.6609 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333
iter=47 0.74564 1.6609 0 0.013333 0 0.013333 0 0 0.013333 0 0.013333 0 0 0.013333 0 0.013333 0
iter=48 0.70974 1.6609 0.013333 0 0.013333 0 0.013333 0.013333 0 0.013333 0 0.013333 0.013333 0 0.013333 0 0.013333
iter=49 0.67549 1.6609 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333 0
iter=50 0.64274 1.6609 0 0.013333 0 0 0.013333 0 0.013333 0 0 0.013333 0 0.013333 0 0 0.013333
iter=51 0.61134 1.6609 0.013333 0 0 0.013333 0.013333 0.013333 0 0 0.013333 0.013333 0.013333 0 0 0.013333 0.013333
iter=52 0.58127 1.6609 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333
iter=53 0.55243 1.6609 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0
iter=54 0.52475 1.6609 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333 0
iter=55 0.49815 1.6609 0.013333 0 0 0 0.013333 0.013333 0 0 0 0.013333 0.013333 0 0 0 0.013333
iter=56 0.47262 1.6609 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0
iter=57 0.44812 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=58 0.42461 1.6609 0 0 0.013333 0.013333 0 0 0 0.013333 0.013333 0 0 0 0.013333 0.013333 0
iter=59 0.40209 1.6609 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333
iter=60 0.38054 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=61 0.35996 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=62 0.3403 1.6609 0 0.013333 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0 0
iter=63 0.32156 2.3488 0 0 0 0.026667 0 0 0 0 0.026667 0 0 0 0 0.026667 0
iter=64 0.30371 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=65 0.28674 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=66 0.27061 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=67 0.25531 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=68 0.2408 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=69 0.22704 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=70 0.21402 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=71 0.2017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=72 0.19006 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=73 0.17904 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=74 0.16864 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=75 0.15882 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=76 0.14955 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=77 0.1408 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=78 0.13254 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=79 0.12476 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=80 0.11742 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=81 0.1105 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=82 0.10398 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=83 0.097838 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=84 0.092051 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=85 0.086601 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=86 0.081469 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=87 0.076637 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=88 0.072088 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=89 0.067805 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tb_val: V(a,z) value at each state space point
zi1_zr_0_025_zw_0_33942 zi2_zr_0_025_zw_0_5596 zi3_zr_0_025_zw_0_92263 zi4_zr_0_025_zw_1_5212 zi5_zr_0_025_zw_2_508 zi6_zr_0_06_zw_0_33942 zi7_zr_0_06_zw_0_5596 zi8_zr_0_06_zw_0_92263 zi9_zr_0_06_zw_1_5212 zi10_zr_0_06_zw_2_508 zi11_zr_0_095_zw_0_33942 zi12_zr_0_095_zw_0_5596 zi13_zr_0_095_zw_0_92263 zi14_zr_0_095_zw_1_5212 zi15_zr_0_095_zw_2_508
_______________________ ______________________ _______________________ ______________________ _____________________ ______________________ _____________________ ______________________ _____________________ _____________________ ________________________ _______________________ ________________________ _______________________ ______________________
a1=-20 -18.809 -17.407 -15.294 -13.317 -10.304 -18.809 -17.407 -15.849 -13.876 -10.785 -18.809 -17.407 -15.849 -14.415 -11.392
a2=-19.0411 -17.247 -15.914 -14.447 -12.632 -9.4616 -18.809 -16.793 -14.884 -13.134 -9.9416 -18.809 -17.407 -15.849 -13.509 -10.541
a3=-18.0822 -16.61 -15.444 -13.965 -11.825 -8.6469 -16.956 -15.711 -14.318 -12.276 -9.0896 -17.691 -16.188 -14.604 -12.775 -9.6088
a4=-17.1233 -15.994 -14.654 -13.175 -11.103 -7.8244 -16.5 -15.331 -13.533 -11.508 -8.2666 -16.738 -15.546 -14.204 -11.925 -8.7072
a5=-16.1644 -15.256 -14.09 -12.604 -10.343 -6.9898 -15.68 -14.429 -12.998 -10.706 -7.4369 -16.204 -14.791 -13.257 -11.164 -7.8125
a6=-15.2055 -14.61 -13.33 -11.863 -9.6209 -6.103 -14.932 -13.856 -12.156 -9.9467 -6.5962 -15.379 -14.172 -12.678 -10.369 -6.9173
a7=-14.2466 -13.9 -12.728 -11.215 -8.8908 -5.1663 -14.277 -13.089 -11.515 -9.1821 -5.704 -14.661 -13.365 -11.885 -9.6156 -5.9788
a8=-13.2877 -13.179 -11.973 -10.477 -8.081 -4.2372 -13.56 -12.383 -10.756 -8.3719 -4.7351 -13.89 -12.721 -11.128 -8.7864 -4.9977
a9=-12.3288 -12.481 -11.315 -9.6894 -7.1681 -3.31 -12.832 -11.676 -10.014 -7.4583 -3.7326 -13.116 -11.929 -10.329 -7.804 -4.0304
a10=-11.3699 -11.737 -10.569 -8.8809 -6.2673 -2.3639 -12.128 -10.886 -9.2232 -6.5477 -2.7212 -12.373 -11.238 -9.491 -6.8365 -3.0699
a11=-10.411 -11.034 -9.8619 -8.0584 -5.3751 -1.4136 -11.378 -10.139 -8.412 -5.6496 -1.7138 -11.589 -10.462 -8.6392 -5.8908 -2.0948
a12=-9.45205 -10.287 -9.1078 -7.233 -4.4969 -0.46125 -10.644 -9.3495 -7.5873 -4.7604 -0.71103 -10.853 -9.7065 -7.7797 -4.9613 -1.0642
a13=-8.49315 -9.5665 -8.3601 -6.404 -3.6155 0.47175 -9.8705 -8.5691 -6.7602 -3.8855 0.26661 -10.075 -8.8589 -6.9224 -4.0518 -0.0023497
a14=-7.53425 -8.7964 -7.5605 -5.5635 -2.6411 1.4272 -9.0536 -7.7398 -5.8632 -2.9911 1.2618 -9.3275 -7.9745 -6.0658 -3.1441 1.0589
a15=-6.57534 -8.0216 -6.7326 -4.7003 -1.479 2.2706 -8.237 -6.8847 -4.9444 -1.7541 2.1408 -8.5285 -7.0737 -5.2012 -2.1371 1.9907
a16=-5.61644 -7.2167 -5.8886 -3.6317 -0.38738 3.0307 -7.3947 -6.0157 -3.8272 -0.59839 2.933 -7.6203 -6.1665 -4.0756 -0.86567 2.8257
a17=-4.65753 -6.3557 -4.9828 -2.4737 0.60261 3.6916 -6.5 -5.0869 -2.626 0.44692 3.6228 -6.6725 -5.2052 -2.8069 0.26485 3.5507
a18=-3.69863 -5.4505 -3.9496 -1.3854 1.5011 4.2901 -5.5643 -4.0925 -1.4994 1.3935 4.2476 -5.6934 -4.1831 -1.6269 1.276 4.2048
a19=-2.73973 -4.5039 -2.9184 -0.36632 2.3172 4.7864 -4.5899 -3.0739 -0.44614 2.2517 4.7676 -4.6831 -3.1405 -0.5308 2.1844 4.7495
a20=-1.78082 -3.5319 -1.9048 0.58667 3.0549 5.2448 -3.5927 -2.0159 0.53752 3.0266 5.2448 -3.6558 -2.1048 0.48783 2.9989 5.2448
a21=-0.821918 -2.55 -0.72707 1.5625 3.6999 5.6293 -2.5878 -0.77398 1.5409 3.6999 5.6293 -2.6255 -0.82049 1.5201 3.6999 5.6293
a22=0 -1.5699 0.22988 2.3102 4.1611 5.955 -1.5894 0.22988 2.3102 4.1611 5.955 -1.6083 0.22988 2.3102 4.1611 5.955
a23=0.136986 -1.4544 0.42786 2.4167 4.2142 5.9967 -1.4544 0.42786 2.4167 4.2142 5.9967 -1.4544 0.42786 2.4167 4.2142 5.9967
a24=1.09589 -0.34206 1.2141 2.9567 4.6541 6.3419 -0.34206 1.2141 2.9567 4.6541 6.3419 -0.34206 1.2141 2.9567 4.6541 6.3419
a25=2.05479 0.59383 1.9235 3.4527 5.0613 6.6701 0.59383 1.9235 3.4527 5.0613 6.6701 0.59383 1.9235 3.4527 5.0613 6.6701
a26=3.0137 1.4012 2.5638 3.9091 5.4394 6.9875 1.4012 2.5638 3.9091 5.4394 6.9875 1.4012 2.5638 3.9091 5.4394 6.9875
a27=3.9726 2.1099 3.143 4.3505 5.8055 7.2941 2.1099 3.143 4.3505 5.8055 7.2941 2.1099 3.143 4.3505 5.8055 7.2941
a28=4.93151 2.7399 3.673 4.7786 6.1605 7.5891 2.7399 3.673 4.7786 6.1605 7.5891 2.7399 3.673 4.7786 6.1605 7.5891
a29=5.89041 3.3067 4.1629 5.1908 6.5027 7.8724 3.3067 4.1629 5.1908 6.5027 7.8724 3.3067 4.1629 5.1908 6.5027 7.8724
a30=6.84932 3.8228 4.6194 5.5859 6.8313 8.1439 3.8228 4.6194 5.5859 6.8313 8.1439 3.8228 4.6194 5.5859 6.8313 8.1439
a31=7.80822 4.2974 5.0471 5.9635 7.1462 8.4041 4.2974 5.0471 5.9635 7.1462 8.4041 4.2974 5.0471 5.9635 7.1462 8.4041
a32=8.76712 4.7375 5.4495 6.3238 7.4474 8.6534 4.7375 5.4495 6.3238 7.4474 8.6534 4.7375 5.4495 6.3238 7.4474 8.6534
a33=9.72603 5.1485 5.8292 6.6674 7.7355 8.8924 5.1485 5.8292 6.6674 7.7355 8.8924 5.1485 5.8292 6.6674 7.7355 8.8924
a34=10.6849 5.5343 6.1885 6.9948 8.011 9.1216 5.5343 6.1885 6.9948 8.011 9.1216 5.5343 6.1885 6.9948 8.011 9.1216
a35=11.6438 5.8979 6.5292 7.3069 8.2745 9.3417 5.8979 6.5292 7.3069 8.2745 9.3417 5.8979 6.5292 7.3069 8.2745 9.3417
a36=12.6027 6.2419 6.8528 7.6046 8.5267 9.5533 6.2419 6.8528 7.6046 8.5267 9.5533 6.2419 6.8528 7.6046 8.5267 9.5533
a37=13.5616 6.5681 7.1607 7.8886 8.7682 9.757 6.5681 7.1607 7.8886 8.7682 9.757 6.5681 7.1607 7.8886 8.7682 9.757
a38=14.5205 6.8782 7.454 8.1597 8.9997 9.9537 6.8782 7.454 8.1597 8.9997 9.9537 6.8782 7.454 8.1597 8.9997 9.9537
a39=15.4795 7.1804 7.7337 8.4189 9.222 10.144 7.1804 7.7337 8.4189 9.222 10.144 7.1804 7.7337 8.4189 9.222 10.144
a40=16.4384 7.4708 8.0011 8.6668 9.4355 10.33 7.4708 8.0011 8.6668 9.4355 10.33 7.4708 8.0011 8.6668 9.4355 10.33
a41=17.3973 7.7515 8.257 8.9041 9.6412 10.512 7.7515 8.257 8.9041 9.6412 10.512 7.7515 8.257 8.9041 9.6412 10.512
a42=18.3562 8.0209 8.5023 9.1316 9.844 10.691 8.0209 8.5023 9.1316 9.844 10.691 8.0209 8.5023 9.1316 9.844 10.691
a43=19.3151 8.2805 8.739 9.3505 10.043 10.865 8.2805 8.739 9.3505 10.043 10.865 8.2805 8.739 9.3505 10.043 10.865
a44=20.274 8.5296 8.971 9.5616 10.237 11.035 8.5296 8.971 9.5616 10.237 11.035 8.5296 8.971 9.5616 10.237 11.035
a45=21.2329 8.7698 9.1949 9.7659 10.426 11.202 8.7698 9.1949 9.7659 10.426 11.202 8.7698 9.1949 9.7659 10.426 11.202
a46=22.1918 9.0024 9.4134 9.9638 10.609 11.366 9.0024 9.4134 9.9638 10.609 11.366 9.0024 9.4134 9.9638 10.609 11.366
a47=23.1507 9.2268 9.6244 10.156 10.788 11.528 9.2268 9.6244 10.156 10.788 11.528 9.2268 9.6244 10.156 10.788 11.528
a48=24.1096 9.4449 9.8301 10.342 10.962 11.685 9.4449 9.8301 10.342 10.962 11.685 9.4449 9.8301 10.342 10.962 11.685
a49=25.0685 9.6555 10.029 10.523 11.131 11.838 9.6555 10.029 10.523 11.131 11.838 9.6555 10.029 10.523 11.131 11.838
a50=26.0274 9.8604 10.223 10.699 11.295 11.987 9.8604 10.223 10.699 11.295 11.987 9.8604 10.223 10.699 11.295 11.987
a51=26.9863 10.058 10.41 10.87 11.455 12.132 10.058 10.41 10.87 11.455 12.132 10.058 10.41 10.87 11.455 12.132
a52=27.9452 10.251 10.593 11.037 11.611 12.274 10.251 10.593 11.037 11.611 12.274 10.251 10.593 11.037 11.611 12.274
a53=28.9041 10.438 10.77 11.2 11.763 12.411 10.438 10.77 11.2 11.763 12.411 10.438 10.77 11.2 11.763 12.411
a54=29.863 10.62 10.943 11.361 11.911 12.546 10.62 10.943 11.361 11.911 12.546 10.62 10.943 11.361 11.911 12.546
a55=30.8219 10.796 11.111 11.518 12.055 12.678 10.796 11.111 11.518 12.055 12.678 10.796 11.111 11.518 12.055 12.678
a56=31.7808 10.968 11.275 11.672 12.197 12.807 10.968 11.275 11.672 12.197 12.807 10.968 11.275 11.672 12.197 12.807
a57=32.7397 11.135 11.434 11.822 12.335 12.933 11.135 11.434 11.822 12.335 12.933 11.135 11.434 11.822 12.335 12.933
a58=33.6986 11.298 11.59 11.97 12.471 13.056 11.298 11.59 11.97 12.471 13.056 11.298 11.59 11.97 12.471 13.056
a59=34.6575 11.456 11.742 12.114 12.603 13.178 11.456 11.742 12.114 12.603 13.178 11.456 11.742 12.114 12.603 13.178
a60=35.6164 11.61 11.891 12.255 12.734 13.297 11.61 11.891 12.255 12.734 13.297 11.61 11.891 12.255 12.734 13.297
a61=36.5753 11.761 12.036 12.394 12.861 13.413 11.761 12.036 12.394 12.861 13.413 11.761 12.036 12.394 12.861 13.413
a62=37.5342 11.908 12.178 12.529 12.986 13.527 11.908 12.178 12.529 12.986 13.527 11.908 12.178 12.529 12.986 13.527
a63=38.4932 12.051 12.317 12.662 13.108 13.639 12.051 12.317 12.662 13.108 13.639 12.051 12.317 12.662 13.108 13.639
a64=39.4521 12.192 12.452 12.791 13.228 13.749 12.192 12.452 12.791 13.228 13.749 12.192 12.452 12.791 13.228 13.749
a65=40.411 12.329 12.585 12.918 13.346 13.857 12.329 12.585 12.918 13.346 13.857 12.329 12.585 12.918 13.346 13.857
a66=41.3699 12.463 12.715 13.043 13.461 13.962 12.463 12.715 13.043 13.461 13.962 12.463 12.715 13.043 13.461 13.962
a67=42.3288 12.594 12.842 13.165 13.574 14.066 12.594 12.842 13.165 13.574 14.066 12.594 12.842 13.165 13.574 14.066
a68=43.2877 12.723 12.967 13.284 13.685 14.168 12.723 12.967 13.284 13.685 14.168 12.723 12.967 13.284 13.685 14.168
a69=44.2466 12.85 13.088 13.401 13.793 14.268 12.85 13.088 13.401 13.793 14.268 12.85 13.088 13.401 13.793 14.268
a70=45.2055 12.975 13.208 13.516 13.9 14.365 12.975 13.208 13.516 13.9 14.365 12.975 13.208 13.516 13.9 14.365
a71=46.1644 13.097 13.325 13.628 14.004 14.462 13.097 13.325 13.628 14.004 14.462 13.097 13.325 13.628 14.004 14.462
a72=47.1233 13.217 13.44 13.739 14.107 14.556 13.217 13.44 13.739 14.107 14.556 13.217 13.44 13.739 14.107 14.556
a73=48.0822 13.335 13.552 13.847 14.207 14.649 13.335 13.552 13.847 14.207 14.649 13.335 13.552 13.847 14.207 14.649
a74=49.0411 13.45 13.663 13.953 14.307 14.741 13.45 13.663 13.953 14.307 14.741 13.45 13.663 13.953 14.307 14.741
a75=50 13.564 13.772 14.056 14.405 14.831 13.564 13.772 14.056 14.405 14.831 13.564 13.772 14.056 14.405 14.831
tb_pol_a: optimal asset choice for each state space point
zi1_zr_0_025_zw_0_33942 zi2_zr_0_025_zw_0_5596 zi3_zr_0_025_zw_0_92263 zi4_zr_0_025_zw_1_5212 zi5_zr_0_025_zw_2_508 zi6_zr_0_06_zw_0_33942 zi7_zr_0_06_zw_0_5596 zi8_zr_0_06_zw_0_92263 zi9_zr_0_06_zw_1_5212 zi10_zr_0_06_zw_2_508 zi11_zr_0_095_zw_0_33942 zi12_zr_0_095_zw_0_5596 zi13_zr_0_095_zw_0_92263 zi14_zr_0_095_zw_1_5212 zi15_zr_0_095_zw_2_508
_______________________ ______________________ _______________________ ______________________ _____________________ ______________________ _____________________ ______________________ _____________________ _____________________ ________________________ _______________________ ________________________ _______________________ ______________________
a1=-20 0 0 -19.512 -19.512 -17.641 0 0 0 -18.868 -17.963 0 0 0 0 -18.265
a2=-19.0411 -19.512 -19.512 -19.512 -18.577 -16.706 0 -18.868 -18.868 -17.963 -17.059 0 0 0 -18.265 -17.389
a3=-18.0822 -19.512 -19.512 -17.641 -17.641 -15.77 -18.868 -18.868 -18.868 -17.059 -16.154 -18.265 -18.265 -18.265 -17.389 -15.638
a4=-17.1233 -17.641 -17.641 -17.641 -16.706 -14.835 -18.868 -17.059 -17.059 -16.154 -15.249 -18.265 -18.265 -18.265 -16.513 -14.762
a5=-16.1644 -16.706 -16.706 -15.77 -15.77 -13.899 -17.059 -17.059 -16.154 -15.249 -14.345 -16.513 -16.513 -16.513 -15.638 -13.886
a6=-15.2055 -15.77 -15.77 -15.77 -14.835 -12.964 -16.154 -16.154 -15.249 -14.345 -13.44 -15.638 -15.638 -14.762 -14.762 -13.011
a7=-14.2466 -14.835 -14.835 -13.899 -13.899 -12.028 -15.249 -15.249 -14.345 -13.44 -12.536 -14.762 -14.762 -14.762 -13.886 -12.135
a8=-13.2877 -13.899 -13.899 -12.964 -12.028 -11.093 -14.345 -13.44 -13.44 -12.536 -10.726 -13.886 -13.886 -13.011 -12.135 -11.259
a9=-12.3288 -12.964 -12.964 -12.028 -11.093 -10.157 -13.44 -12.536 -12.536 -11.631 -9.8217 -13.011 -13.011 -12.135 -11.259 -10.383
a10=-11.3699 -12.028 -12.028 -11.093 -10.157 -9.2215 -12.536 -11.631 -11.631 -10.726 -8.917 -12.135 -12.135 -11.259 -10.383 -9.5077
a11=-10.411 -11.093 -11.093 -10.157 -9.2215 -8.286 -11.631 -10.726 -10.726 -9.8217 -8.0124 -11.259 -11.259 -10.383 -9.5077 -8.632
a12=-9.45205 -10.157 -10.157 -9.2215 -8.286 -7.3505 -9.8217 -9.8217 -9.8217 -8.917 -7.1078 -10.383 -9.5077 -9.5077 -8.632 -6.8806
a13=-8.49315 -9.2215 -9.2215 -8.286 -7.3505 -6.415 -8.917 -8.917 -8.917 -8.0124 -6.2032 -9.5077 -8.632 -8.632 -7.7563 -6.0049
a14=-7.53425 -8.286 -8.286 -7.3505 -6.415 -5.4795 -8.0124 -8.0124 -7.1078 -6.2032 -5.2985 -8.632 -7.7563 -7.7563 -6.8806 -5.1292
a15=-6.57534 -7.3505 -7.3505 -6.415 -5.4795 -4.5439 -7.1078 -7.1078 -6.2032 -5.2985 -4.3939 -6.8806 -6.8806 -6.8806 -5.1292 -4.2535
a16=-5.61644 -6.415 -6.415 -5.4795 -4.5439 -3.6084 -6.2032 -6.2032 -5.2985 -4.3939 -3.4893 -6.0049 -6.0049 -5.1292 -4.2535 -3.3777
a17=-4.65753 -5.4795 -5.4795 -4.5439 -3.6084 -2.6729 -5.2985 -5.2985 -4.3939 -3.4893 -2.5846 -5.1292 -5.1292 -4.2535 -3.3777 -2.502
a18=-3.69863 -4.5439 -3.6084 -3.6084 -2.6729 -1.7374 -4.3939 -4.3939 -3.4893 -2.5846 -1.68 -4.2535 -4.2535 -3.3777 -2.502 -1.6263
a19=-2.73973 -3.6084 -2.6729 -2.6729 -1.7374 -0.80187 -3.4893 -3.4893 -2.5846 -1.68 -0.77539 -3.3777 -3.3777 -2.502 -1.6263 -0.75061
a20=-1.78082 -2.6729 -1.7374 -1.7374 -0.80187 0 -2.5846 -1.68 -1.68 -0.77539 0 -2.502 -2.502 -1.6263 -0.75061 0
a21=-0.821918 -1.7374 -0.80187 -0.80187 0 0.13365 -1.68 -0.77539 -0.77539 0 0.13365 -1.6263 -0.75061 -0.75061 0 0.13365
a22=0 -0.80187 0 0 0.13365 1.0692 -0.77539 0 0 0.13365 1.0692 -0.75061 0 0 0.13365 1.0692
a23=0.136986 0 0 0.13365 0.13365 1.0692 0 0 0.13365 0.13365 1.0692 0 0 0.13365 0.13365 1.0692
a24=1.09589 0.13365 0.13365 1.0692 1.0692 2.0047 0.13365 0.13365 1.0692 1.0692 2.0047 0.13365 0.13365 1.0692 1.0692 2.0047
a25=2.05479 1.0692 1.0692 2.0047 2.0047 2.9402 1.0692 1.0692 2.0047 2.0047 2.9402 1.0692 1.0692 2.0047 2.0047 2.9402
a26=3.0137 2.0047 2.0047 2.9402 2.9402 3.8757 2.0047 2.0047 2.9402 2.9402 3.8757 2.0047 2.0047 2.9402 2.9402 3.8757
a27=3.9726 2.9402 2.9402 2.9402 3.8757 4.8112 2.9402 2.9402 2.9402 3.8757 4.8112 2.9402 2.9402 2.9402 3.8757 4.8112
a28=4.93151 3.8757 3.8757 3.8757 4.8112 5.7467 3.8757 3.8757 3.8757 4.8112 5.7467 3.8757 3.8757 3.8757 4.8112 5.7467
a29=5.89041 4.8112 4.8112 4.8112 5.7467 6.6823 4.8112 4.8112 4.8112 5.7467 6.6823 4.8112 4.8112 4.8112 5.7467 6.6823
a30=6.84932 5.7467 5.7467 5.7467 6.6823 7.6178 5.7467 5.7467 5.7467 6.6823 7.6178 5.7467 5.7467 5.7467 6.6823 7.6178
a31=7.80822 6.6823 6.6823 6.6823 7.6178 8.5533 6.6823 6.6823 6.6823 7.6178 8.5533 6.6823 6.6823 6.6823 7.6178 8.5533
a32=8.76712 7.6178 7.6178 7.6178 8.5533 9.4888 7.6178 7.6178 7.6178 8.5533 9.4888 7.6178 7.6178 7.6178 8.5533 9.4888
a33=9.72603 8.5533 8.5533 8.5533 9.4888 10.424 8.5533 8.5533 8.5533 9.4888 10.424 8.5533 8.5533 8.5533 9.4888 10.424
a34=10.6849 9.4888 9.4888 9.4888 10.424 11.36 9.4888 9.4888 9.4888 10.424 11.36 9.4888 9.4888 9.4888 10.424 11.36
a35=11.6438 10.424 10.424 10.424 11.36 12.295 10.424 10.424 10.424 11.36 12.295 10.424 10.424 10.424 11.36 12.295
a36=12.6027 11.36 11.36 11.36 12.295 13.231 11.36 11.36 11.36 12.295 13.231 11.36 11.36 11.36 12.295 13.231
a37=13.5616 12.295 12.295 12.295 13.231 14.166 12.295 12.295 12.295 13.231 14.166 12.295 12.295 12.295 13.231 14.166
a38=14.5205 13.231 13.231 13.231 14.166 15.102 13.231 13.231 13.231 14.166 15.102 13.231 13.231 13.231 14.166 15.102
a39=15.4795 13.231 14.166 14.166 15.102 16.037 13.231 14.166 14.166 15.102 16.037 13.231 14.166 14.166 15.102 16.037
a40=16.4384 14.166 15.102 15.102 16.037 16.973 14.166 15.102 15.102 16.037 16.973 14.166 15.102 15.102 16.037 16.973
a41=17.3973 15.102 16.037 16.037 16.973 17.908 15.102 16.037 16.037 16.973 17.908 15.102 16.037 16.037 16.973 17.908
a42=18.3562 16.037 16.973 16.973 16.973 18.844 16.037 16.973 16.973 16.973 18.844 16.037 16.973 16.973 16.973 18.844
a43=19.3151 16.973 16.973 17.908 17.908 19.779 16.973 16.973 17.908 17.908 19.779 16.973 16.973 17.908 17.908 19.779
a44=20.274 17.908 17.908 18.844 18.844 20.715 17.908 17.908 18.844 18.844 20.715 17.908 17.908 18.844 18.844 20.715
a45=21.2329 18.844 18.844 19.779 19.779 21.651 18.844 18.844 19.779 19.779 21.651 18.844 18.844 19.779 19.779 21.651
a46=22.1918 19.779 19.779 20.715 20.715 21.651 19.779 19.779 20.715 20.715 21.651 19.779 19.779 20.715 20.715 21.651
a47=23.1507 20.715 20.715 21.651 21.651 22.586 20.715 20.715 21.651 21.651 22.586 20.715 20.715 21.651 21.651 22.586
a48=24.1096 21.651 21.651 22.586 22.586 23.522 21.651 21.651 22.586 22.586 23.522 21.651 21.651 22.586 22.586 23.522
a49=25.0685 22.586 22.586 23.522 23.522 24.457 22.586 22.586 23.522 23.522 24.457 22.586 22.586 23.522 23.522 24.457
a50=26.0274 23.522 23.522 24.457 24.457 25.393 23.522 23.522 24.457 24.457 25.393 23.522 23.522 24.457 24.457 25.393
a51=26.9863 24.457 24.457 25.393 25.393 26.328 24.457 24.457 25.393 25.393 26.328 24.457 24.457 25.393 25.393 26.328
a52=27.9452 25.393 25.393 26.328 26.328 27.264 25.393 25.393 26.328 26.328 27.264 25.393 25.393 26.328 26.328 27.264
a53=28.9041 26.328 26.328 26.328 27.264 28.199 26.328 26.328 26.328 27.264 28.199 26.328 26.328 26.328 27.264 28.199
a54=29.863 27.264 27.264 27.264 28.199 29.135 27.264 27.264 27.264 28.199 29.135 27.264 27.264 27.264 28.199 29.135
a55=30.8219 28.199 28.199 28.199 29.135 30.07 28.199 28.199 28.199 29.135 30.07 28.199 28.199 28.199 29.135 30.07
a56=31.7808 29.135 29.135 29.135 30.07 31.006 29.135 29.135 29.135 30.07 31.006 29.135 29.135 29.135 30.07 31.006
a57=32.7397 30.07 30.07 30.07 31.006 31.941 30.07 30.07 30.07 31.006 31.941 30.07 30.07 30.07 31.006 31.941
a58=33.6986 31.006 31.006 31.006 31.941 32.877 31.006 31.006 31.006 31.941 32.877 31.006 31.006 31.006 31.941 32.877
a59=34.6575 31.941 31.941 31.941 32.877 33.812 31.941 31.941 31.941 32.877 33.812 31.941 31.941 31.941 32.877 33.812
a60=35.6164 32.877 32.877 32.877 33.812 34.748 32.877 32.877 32.877 33.812 34.748 32.877 32.877 32.877 33.812 34.748
a61=36.5753 33.812 33.812 33.812 34.748 35.683 33.812 33.812 33.812 34.748 35.683 33.812 33.812 33.812 34.748 35.683
a62=37.5342 34.748 34.748 34.748 35.683 36.619 34.748 34.748 34.748 35.683 36.619 34.748 34.748 34.748 35.683 36.619
a63=38.4932 35.683 35.683 35.683 36.619 37.554 35.683 35.683 35.683 36.619 37.554 35.683 35.683 35.683 36.619 37.554
a64=39.4521 36.619 36.619 36.619 37.554 38.49 36.619 36.619 36.619 37.554 38.49 36.619 36.619 36.619 37.554 38.49
a65=40.411 37.554 37.554 37.554 38.49 39.425 37.554 37.554 37.554 38.49 39.425 37.554 37.554 37.554 38.49 39.425
a66=41.3699 38.49 38.49 38.49 39.425 40.361 38.49 38.49 38.49 39.425 40.361 38.49 38.49 38.49 39.425 40.361
a67=42.3288 38.49 39.425 39.425 40.361 41.296 38.49 39.425 39.425 40.361 41.296 38.49 39.425 39.425 40.361 41.296
a68=43.2877 39.425 40.361 40.361 41.296 42.232 39.425 40.361 40.361 41.296 42.232 39.425 40.361 40.361 41.296 42.232
a69=44.2466 40.361 41.296 41.296 42.232 43.167 40.361 41.296 41.296 42.232 43.167 40.361 41.296 41.296 42.232 43.167
a70=45.2055 41.296 42.232 42.232 43.167 44.103 41.296 42.232 42.232 43.167 44.103 41.296 42.232 42.232 43.167 44.103
a71=46.1644 42.232 43.167 43.167 44.103 45.038 42.232 43.167 43.167 44.103 45.038 42.232 43.167 43.167 44.103 45.038
a72=47.1233 43.167 44.103 44.103 45.038 45.974 43.167 44.103 44.103 45.038 45.974 43.167 44.103 44.103 45.038 45.974
a73=48.0822 44.103 45.038 45.038 45.038 46.909 44.103 45.038 45.038 45.038 46.909 44.103 45.038 45.038 45.038 46.909
a74=49.0411 45.038 45.038 45.974 45.974 47.845 45.038 45.038 45.974 45.974 47.845 45.038 45.038 45.974 45.974 47.845
a75=50 45.974 45.974 46.909 46.909 48.78 45.974 45.974 46.909 46.909 48.78 45.974 45.974 46.909 46.909 48.78
end
ans =
Map with properties:
Count: 12
KeyType: char
ValueType: any