Solve One Asset Dynamic Programming Problem (Loop)
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Contents
function result_map = ff_az_vf(varargin)
FF_AZ_VF solve infinite horizon exo shock + endo asset problem
This program solves the infinite horizon dynamic single asset and single shock problem with loops. It is useful to have a version of code that is looped for easy debugging. This is the standard dynamic exogenous incomplete savings problem.
See ff_abz_vf for the version of the problem that accommodates both borrowing and savings.
@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);
% Change Keys in param_map
param_map('it_a_n') = 50;
param_map('it_z_n') = 5;
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
% Note this program works very slowly if the grid sizes are too large
ff_az_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_az_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('it_z_n') = 15; [armt_map, func_map] = ffs_az_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_az_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_az_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'}); [ar_a, mt_z_trans, ar_z] = params_group{:}; % func_map params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons', 'f_coh'}); [f_util_log, f_util_crra, f_cons, f_coh] = params_group{:}; % param_map params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_nan_replace'}); [it_a_n, it_z_n, fl_crra, fl_beta, fl_nan_replace] = 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', 'it_display_every', 'bl_post'}); [bl_profile, st_profile_path, ... st_profile_prefix, st_profile_name_main, st_profile_suffix, ... bl_time, bl_display, it_display_every, bl_post] = params_group{:};
Initialize Output Matrixes
mt_val_cur = zeros(length(ar_a),length(ar_z)); mt_val = mt_val_cur - 1; mt_pol_a = zeros(length(ar_a),length(ar_z)); 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 % Value Function Iteration while bl_vfi_continue
it_iter = it_iter + 1;
Solve Optimization Problem Current Iteration
% loop 1: over exogenous states for it_z_i = 1:length(ar_z) fl_z = ar_z(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)); % loop 3: over choices for it_ap_k = 1:length(ar_a) fl_ap = ar_a(it_ap_k); fl_c = f_cons(fl_z, fl_a, fl_ap); % 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_zp_q = 1:length(ar_z) ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + fl_beta*mt_z_trans(it_z_i,it_zp_q)*mt_val_cur(it_ap_k,it_zp_q); end % Replace if negative consumption if fl_c <= 0 ar_val_cur(it_ap_k) = fl_nan_replace; 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_a_j,it_z_i) = ar_val_cur(it_max_lin_idx(1)); mt_pol_a(it_a_j,it_z_i) = ar_a(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); 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
Process Optimal Choices
for choices outcomes, store as cell with two elements, first element is the y(a,z), outcome given states, the second element will be solved found in ff_ds_vf and other distributions files. It stores what are the probability mass function of y, along with sorted unique values of y.
result_map = containers.Map('KeyType','char', 'ValueType','any'); result_map('mt_val') = mt_val; result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)}; result_map('cl_mt_coh') = {f_coh(ar_z, ar_a'), zeros(1)}; result_map('cl_mt_pol_c') = {f_coh(ar_z, ar_a') - mt_pol_a, zeros(1)}; result_map('ar_st_pol_names') = ["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 z1_0_34741 z2_0_40076 z3_0_4623 z4_0_5333 z5_0_61519 z6_0_70966 z10_1_2567 z11_1_4496 z12_1_6723 z13_1_9291 z14_2_2253 z15_2_567
________ _______ __________ __________ _________ _________ __________ __________ __________ __________ __________ __________ __________ _________
iter=1 51.663 33.541 1 1 1 1 1 1 1 1 1 1 1 1
iter=2 39.232 484.82 0.97333 0.97333 0.97333 0.97333 0.97333 0.97333 0.98667 0.98667 0.98667 0.98667 0.98667 0.98667
iter=3 32.201 161.77 0.94667 0.94667 0.94667 0.94667 0.94667 0.94667 0.96 0.96 0.96 0.96 0.98667 0.98667
iter=4 27.151 81.566 0.90667 0.90667 0.90667 0.90667 0.90667 0.90667 0.92 0.92 0.92 0.92 0.96 0.94667
iter=5 23.25 49.094 0.85333 0.85333 0.85333 0.85333 0.85333 0.85333 0.85333 0.86667 0.86667 0.89333 0.90667 0.92
iter=6 20.117 32.814 0.78667 0.78667 0.78667 0.78667 0.78667 0.78667 0.78667 0.8 0.8 0.84 0.84 0.85333
iter=7 17.537 23.546 0.70667 0.70667 0.70667 0.70667 0.70667 0.70667 0.72 0.72 0.72 0.78667 0.76 0.74667
iter=8 15.378 17.598 0.53333 0.56 0.57333 0.61333 0.61333 0.61333 0.61333 0.61333 0.62667 0.68 0.66667 0.68
iter=9 13.546 13.725 0.44 0.41333 0.44 0.44 0.48 0.50667 0.48 0.49333 0.52 0.57333 0.54667 0.58667
iter=10 11.978 11.145 0.33333 0.34667 0.34667 0.34667 0.34667 0.38667 0.4 0.4 0.42667 0.44 0.45333 0.48
iter=11 10.624 9.3002 0.28 0.26667 0.28 0.28 0.30667 0.32 0.32 0.32 0.34667 0.36 0.34667 0.42667
iter=12 9.4485 7.2682 0.24 0.22667 0.2 0.22667 0.21333 0.21333 0.25333 0.26667 0.28 0.30667 0.30667 0.29333
iter=13 8.4217 6.2658 0.17333 0.18667 0.2 0.2 0.2 0.21333 0.21333 0.21333 0.24 0.25333 0.25333 0.28
iter=14 7.5211 5.22 0.17333 0.17333 0.16 0.16 0.13333 0.14667 0.2 0.17333 0.18667 0.2 0.21333 0.21333
iter=15 6.7283 4.5688 0.13333 0.13333 0.13333 0.12 0.14667 0.16 0.13333 0.14667 0.18667 0.17333 0.17333 0.22667
iter=16 6.0276 4.2847 0.12 0.12 0.12 0.13333 0.13333 0.13333 0.14667 0.14667 0.13333 0.16 0.18667 0.14667
iter=17 5.4072 3.6778 0.093333 0.12 0.13333 0.13333 0.10667 0.066667 0.13333 0.12 0.13333 0.13333 0.093333 0.14667
iter=18 4.8571 3.1396 0.10667 0.08 0.053333 0.053333 0.08 0.08 0.10667 0.08 0.10667 0.12 0.12 0.14667
iter=19 4.3673 2.6864 0.053333 0.08 0.08 0.08 0.066667 0.08 0.066667 0.093333 0.10667 0.093333 0.093333 0.10667
iter=20 3.9302 2.6727 0.066667 0.053333 0.066667 0.066667 0.066667 0.093333 0.08 0.08 0.10667 0.08 0.10667 0.093333
iter=21 3.5404 2.1691 0.04 0.053333 0.053333 0.053333 0.08 0.066667 0.066667 0.066667 0.066667 0.08 0.08 0.066667
iter=22 3.1927 2.202 0.053333 0.053333 0.053333 0.066667 0.066667 0.066667 0.066667 0.08 0.053333 0.053333 0.066667 0.066667
iter=23 2.882 2.1292 0.04 0.04 0.053333 0.053333 0.053333 0.026667 0.053333 0.053333 0.04 0.066667 0.053333 0.08
iter=24 2.6037 2.2502 0.04 0.04 0.053333 0.026667 0.013333 0.04 0.066667 0.026667 0.053333 0.066667 0.053333 0.08
iter=25 2.3541 2.2001 0.04 0.04 0.026667 0.04 0.04 0.013333 0.04 0.04 0.026667 0.066667 0.04 0.053333
iter=26 2.1298 1.8083 0.04 0.026667 0.026667 0.026667 0.026667 0.04 0.013333 0.04 0.066667 0.026667 0.04 0.053333
iter=27 1.9284 1.4431 0.013333 0.026667 0.013333 0.013333 0.013333 0.026667 0.04 0.026667 0.026667 0.026667 0.04 0.013333
iter=28 1.7477 1.4431 0.013333 0.013333 0.013333 0.013333 0.026667 0.013333 0.013333 0.026667 0.026667 0.026667 0.04 0.026667
iter=29 1.5856 1.6551 0.026667 0.013333 0.026667 0.026667 0.013333 0.026667 0.026667 0.026667 0.04 0.026667 0.026667 0.026667
iter=30 1.4402 1.4431 0 0.013333 0 0 0.013333 0.013333 0.013333 0.026667 0.04 0.013333 0.026667 0.026667
iter=31 1.3096 1.4431 0.013333 0.013333 0.013333 0.013333 0.026667 0.026667 0.026667 0.013333 0.026667 0.026667 0.04 0.04
iter=32 1.192 1.1703 0.013333 0 0.013333 0.013333 0.013333 0.013333 0.013333 0.04 0.013333 0.013333 0.026667 0.013333
iter=33 1.0863 1.3514 0 0.013333 0.013333 0.026667 0.013333 0.013333 0 0.013333 0 0.026667 0.013333 0.026667
iter=34 0.99098 0.95555 0.013333 0.013333 0 0.013333 0 0.026667 0.013333 0.026667 0.013333 0 0.026667 0
iter=35 0.90512 0.95555 0 0.013333 0.013333 0 0.026667 0 0.026667 0.013333 0.013333 0.013333 0.013333 0.013333
iter=36 0.82778 1.0933 0.013333 0 0.013333 0.013333 0.013333 0.026667 0.013333 0 0 0.013333 0 0.026667
iter=37 0.75813 1.0933 0 0.013333 0.013333 0 0 0.013333 0 0.026667 0.026667 0.026667 0.013333 0.013333
iter=38 0.69538 0.95555 0 0 0 0.013333 0.013333 0 0.013333 0.013333 0 0 0.013333 0
iter=39 0.63885 0.95555 0.013333 0 0.013333 0 0 0.026667 0 0.013333 0.013333 0.013333 0 0.013333
iter=40 0.5879 0.95555 0 0.013333 0 0.013333 0.013333 0.013333 0.013333 0 0 0 0.013333 0
iter=41 0.54193 1.0933 0 0 0 0 0 0 0 0.013333 0 0.013333 0 0.026667
iter=42 0.50037 0.67568 0 0 0 0 0 0 0.013333 0 0 0 0 0
iter=43 0.46276 0.95555 0 0 0.013333 0 0.013333 0.013333 0 0 0.013333 0.013333 0 0.013333
iter=44 0.42864 0.67568 0 0 0 0.013333 0 0 0 0 0 0 0 0
iter=45 0.39761 0.95555 0.013333 0.013333 0 0 0 0 0 0 0 0 0 0.013333
iter=46 0.36934 1.0933 0 0 0 0 0 0 0.026667 0 0 0.013333 0.013333 0
iter=47 0.3435 0.67568 0 0 0 0 0.013333 0 0 0 0 0 0 0
iter=48 0.31982 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=49 0.29808 0.67568 0 0 0 0 0 0 0 0 0 0 0 0.013333
iter=50 0.27807 0.67568 0 0 0 0 0 0 0 0 0.013333 0.013333 0 0
iter=51 0.25962 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=52 0.24257 0.67568 0 0 0.013333 0 0 0 0 0 0 0 0 0
iter=53 0.22679 0.67568 0 0 0 0.013333 0 0 0 0 0 0 0 0
iter=54 0.21216 0.67568 0 0 0 0 0 0 0.013333 0 0 0 0 0
iter=55 0.19858 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=56 0.18595 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=57 0.1742 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=58 0.16325 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=59 0.15304 0.67568 0 0 0 0 0.013333 0 0 0 0 0.013333 0 0
iter=60 0.14351 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=61 0.13461 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=62 0.12629 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=63 0.11851 0.67568 0 0 0 0 0 0 0 0 0 0 0 0.013333
iter=64 0.11123 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=65 0.10441 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=66 0.098024 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=67 0.092041 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=68 0.086433 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=69 0.081176 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=70 0.076245 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=71 0.07162 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=72 0.067281 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=73 0.063208 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=74 0.059386 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=75 0.055798 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=76 0.052429 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=77 0.049266 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=78 0.046295 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=79 0.043505 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=80 0.040885 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=81 0.038423 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=82 0.03611 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=83 0.033937 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=84 0.031896 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=85 0.029978 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=86 0.028176 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=87 0.026482 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=88 0.024891 0 0 0 0 0 0 0 0 0 0 0 0 0
iter=89 0.023395 0 0 0 0 0 0 0 0 0 0 0 0 0
tb_val: V(a,z) value at each state space point
z1_0_34741 z2_0_40076 z3_0_4623 z4_0_5333 z5_0_61519 z6_0_70966 z10_1_2567 z11_1_4496 z12_1_6723 z13_1_9291 z14_2_2253 z15_2_567
__________ __________ _________ _________ __________ __________ __________ __________ __________ __________ __________ _________
a1=0 -1.5593 -0.92269 -0.27457 0.36174 0.97631 1.5665 3.701 4.1898 4.6879 5.2034 5.6887 6.1833
a2=0.675676 -0.43558 0.048209 0.56057 1.0769 1.5861 2.0843 4.0533 4.5206 4.9905 5.488 5.9575 6.432
a3=1.35135 0.4358 0.8321 1.2578 1.6941 2.1328 2.5716 4.3899 4.8371 5.2817 5.7626 6.2171 6.6721
a4=2.02703 1.1476 1.4879 1.8568 2.2393 2.6288 3.0236 4.7121 5.1409 5.5644 6.0276 6.4678 6.9034
a5=2.7027 1.7511 2.0539 2.384 2.7289 3.0829 3.4445 5.0197 5.432 5.8407 6.283 6.7094 7.1261
a6=3.37838 2.2777 2.5541 2.8565 3.1738 3.5009 3.8365 5.3164 5.7129 6.1072 6.5279 6.9414 7.3412
a7=4.05405 2.747 3.004 3.2857 3.5821 3.8886 4.2039 5.6 5.9817 6.3625 6.7632 7.1649 7.5494
a8=4.72973 3.1721 3.4142 3.68 3.9601 4.2503 4.5493 5.8704 6.2385 6.6069 6.9909 7.3812 7.751
a9=5.40541 3.5618 3.7922 4.0453 4.3124 4.5893 4.8746 6.1315 6.4869 6.8434 7.2108 7.5903 7.9465
a10=6.08108 3.9226 4.1435 4.3862 4.6424 4.9081 5.1819 6.3829 6.7265 7.0717 7.423 7.7925 8.1371
a11=6.75676 4.2689 4.4719 4.7058 4.9528 5.2091 5.4733 6.6245 6.9569 7.2916 7.6283 7.9889 8.3233
a12=7.43243 4.5998 4.7916 5.0074 5.2463 5.4944 5.7502 6.8563 7.1785 7.5035 7.8286 8.1804 8.5062
a13=8.10811 4.9124 5.0965 5.3011 5.525 5.7656 6.0139 7.0811 7.3928 7.7092 8.0261 8.3666 8.6851
a14=8.78378 5.2113 5.3871 5.5836 5.7935 6.0245 6.2657 7.3018 7.601 7.9092 8.2183 8.5469 8.8584
a15=9.45946 5.4971 5.6653 5.8539 6.0562 6.2724 6.5068 7.5156 7.8023 8.1028 8.4043 8.7214 9.0262
a16=10.1351 5.7709 5.9321 6.1131 6.308 6.5134 6.7385 7.722 7.9968 8.2899 8.5842 8.8904 9.1889
a17=10.8108 6.0339 6.1889 6.3629 6.5505 6.7489 6.9619 7.9212 8.1846 8.4707 8.7583 9.0545 9.3472
a18=11.4865 6.2864 6.4357 6.6033 6.7841 6.9759 7.1778 8.1135 8.3663 8.6458 8.927 9.2147 9.5017
a19=12.1622 6.5297 6.6739 6.8357 7.0102 7.1956 7.3908 8.2994 8.5448 8.8164 9.0916 9.371 9.6525
a20=12.8378 6.7638 6.9033 7.0596 7.2283 7.4076 7.5969 8.4797 8.7197 8.9828 9.2522 9.5234 9.7995
a21=13.5135 6.9901 7.1252 7.2767 7.4401 7.6138 7.7973 8.655 8.8899 9.1447 9.4086 9.6721 9.9431
a22=14.1892 7.2082 7.3393 7.4863 7.6448 7.8133 7.9914 8.8253 9.0555 9.3024 9.5611 9.8174 10.084
a23=14.8649 7.4195 7.5469 7.6897 7.8437 8.0071 8.1799 8.9912 9.2167 9.4562 9.7099 9.9609 10.221
a24=15.5405 7.6236 7.7476 7.8866 8.0363 8.1954 8.3634 9.1527 9.3737 9.6061 9.8551 10.102 10.355
a25=16.2162 7.8217 7.9425 8.0778 8.2237 8.3785 8.5421 9.3102 9.5268 9.7525 9.9969 10.239 10.487
a26=16.8919 8.0134 8.1313 8.2633 8.4055 8.5565 8.716 9.4638 9.6762 9.8953 10.135 10.373 10.616
a27=17.5676 8.1997 8.3148 8.4437 8.5825 8.7298 8.8853 9.6138 9.8219 10.036 10.271 10.505 10.743
a28=18.2432 8.3804 8.4929 8.6189 8.7546 8.8985 9.0504 9.7605 9.9646 10.175 10.405 10.635 10.867
a29=18.9189 8.5562 8.6663 8.7895 8.9223 9.063 9.2114 9.9042 10.104 10.311 10.535 10.762 10.989
a30=19.5946 8.727 8.8348 8.9555 9.0855 9.2233 9.3686 10.045 10.241 10.444 10.663 10.886 11.108
a31=20.2703 8.8934 8.999 9.1173 9.2447 9.3797 9.522 10.182 10.376 10.575 10.789 11.008 11.226
a32=20.9459 9.0557 9.1589 9.2749 9.3998 9.5322 9.6717 10.317 10.507 10.703 10.912 11.128 11.341
a33=21.6216 9.216 9.3148 9.4287 9.5513 9.6812 9.8181 10.449 10.636 10.829 11.033 11.245 11.454
a34=22.2973 9.3723 9.4681 9.5786 9.6991 9.8267 9.9611 10.579 10.762 10.952 11.151 11.361 11.565
a35=22.973 9.5247 9.6187 9.7252 9.8435 9.9688 10.101 10.706 10.886 11.073 11.268 11.474 11.674
a36=23.6486 9.6739 9.7659 9.8694 9.9846 10.108 10.238 10.831 11.008 11.191 11.382 11.585 11.781
a37=24.3243 9.8197 9.9098 10.011 10.123 10.244 10.371 10.953 11.127 11.308 11.494 11.694 11.886
a38=25 9.9624 10.051 10.15 10.258 10.377 10.502 11.073 11.244 11.422 11.604 11.801 11.99
a39=25.6757 10.102 10.189 10.286 10.392 10.507 10.631 11.192 11.359 11.534 11.713 11.907 12.092
a40=26.3514 10.239 10.324 10.419 10.523 10.635 10.756 11.309 11.472 11.644 11.821 12.011 12.194
a41=27.027 10.373 10.456 10.55 10.651 10.76 10.88 11.423 11.583 11.753 11.927 12.113 12.295
a42=27.7027 10.505 10.586 10.678 10.777 10.884 11 11.536 11.692 11.859 12.031 12.214 12.393
a43=28.3784 10.634 10.713 10.803 10.901 11.006 11.119 11.647 11.8 11.964 12.134 12.314 12.49
a44=29.0541 10.76 10.838 10.926 11.022 11.125 11.235 11.756 11.905 12.068 12.235 12.411 12.586
a45=29.7297 10.884 10.961 11.047 11.142 11.243 11.35 11.862 12.009 12.169 12.334 12.507 12.68
a46=30.4054 11.006 11.081 11.166 11.259 11.358 11.463 11.967 12.111 12.269 12.432 12.602 12.772
a47=31.0811 11.125 11.199 11.283 11.373 11.471 11.575 12.071 12.211 12.367 12.528 12.695 12.863
a48=31.7568 11.243 11.315 11.397 11.487 11.582 11.684 12.172 12.311 12.463 12.622 12.786 12.952
a49=32.4324 11.358 11.429 11.51 11.598 11.692 11.792 12.272 12.409 12.559 12.715 12.877 13.041
a50=33.1081 11.47 11.541 11.62 11.707 11.799 11.898 12.37 12.505 12.652 12.807 12.965 13.128
a51=33.7838 11.582 11.651 11.729 11.814 11.905 12.002 12.466 12.6 12.744 12.897 13.053 13.213
a52=34.4595 11.691 11.759 11.836 11.919 12.009 12.104 12.562 12.693 12.835 12.986 13.139 13.298
a53=35.1351 11.798 11.865 11.941 12.023 12.111 12.205 12.655 12.785 12.925 13.074 13.224 13.381
a54=35.8108 11.903 11.969 12.044 12.125 12.212 12.305 12.747 12.876 13.013 13.16 13.309 13.463
a55=36.4865 12.007 12.072 12.146 12.226 12.311 12.402 12.838 12.965 13.1 13.245 13.392 13.544
a56=37.1622 12.109 12.173 12.246 12.324 12.409 12.499 12.928 13.053 13.185 13.329 13.474 13.624
a57=37.8378 12.209 12.272 12.344 12.422 12.505 12.593 13.016 13.14 13.269 13.412 13.555 13.703
a58=38.5135 12.308 12.37 12.441 12.517 12.599 12.687 13.103 13.225 13.353 13.493 13.635 13.78
a59=39.1892 12.405 12.466 12.536 12.612 12.692 12.779 13.188 13.309 13.436 13.573 13.714 13.857
a60=39.8649 12.5 12.561 12.63 12.704 12.784 12.869 13.273 13.392 13.517 13.653 13.792 13.933
a61=40.5405 12.594 12.654 12.722 12.796 12.875 12.958 13.356 13.474 13.598 13.731 13.869 14.008
a62=41.2162 12.687 12.746 12.813 12.886 12.964 13.046 13.438 13.555 13.677 13.809 13.945 14.082
a63=41.8919 12.779 12.836 12.903 12.974 13.051 13.133 13.519 13.634 13.755 13.885 14.02 14.155
a64=42.5676 12.869 12.925 12.991 13.062 13.138 13.219 13.599 13.713 13.833 13.96 14.094 14.227
a65=43.2432 12.958 13.014 13.078 13.148 13.223 13.303 13.678 13.791 13.909 14.035 14.167 14.298
a66=43.9189 13.046 13.101 13.163 13.233 13.307 13.386 13.756 13.868 13.984 14.108 14.239 14.369
a67=44.5946 13.133 13.187 13.248 13.316 13.39 13.468 13.833 13.943 14.059 14.181 14.31 14.438
a68=45.2703 13.218 13.272 13.332 13.399 13.472 13.549 13.909 14.018 14.132 14.253 14.381 14.507
a69=45.9459 13.302 13.355 13.415 13.48 13.552 13.628 13.984 14.092 14.205 14.324 14.45 14.574
a70=46.6216 13.385 13.438 13.497 13.561 13.631 13.707 14.059 14.165 14.277 14.393 14.519 14.641
a71=47.2973 13.467 13.519 13.577 13.641 13.71 13.785 14.132 14.237 14.347 14.463 14.586 14.707
a72=47.973 13.548 13.599 13.657 13.719 13.787 13.861 14.205 14.308 14.417 14.531 14.653 14.773
a73=48.6486 13.628 13.678 13.735 13.797 13.864 13.937 14.277 14.378 14.486 14.599 14.72 14.838
a74=49.3243 13.707 13.757 13.813 13.874 13.94 14.011 14.348 14.448 14.555 14.666 14.785 14.903
a75=50 13.785 13.834 13.889 13.95 14.014 14.085 14.418 14.516 14.622 14.733 14.85 14.967
tb_pol_a: optimal asset choice for each state space point
z1_0_34741 z2_0_40076 z3_0_4623 z4_0_5333 z5_0_61519 z6_0_70966 z10_1_2567 z11_1_4496 z12_1_6723 z13_1_9291 z14_2_2253 z15_2_567
__________ __________ _________ _________ __________ __________ __________ __________ __________ __________ __________ _________
a1=0 0 0 0 0 0 0 0 0 0.67568 0.67568 0.67568 1.3514
a2=0.675676 0 0 0 0 0 0 0.67568 0.67568 1.3514 1.3514 1.3514 2.027
a3=1.35135 0.67568 0.67568 0.67568 0.67568 0.67568 0.67568 1.3514 1.3514 2.027 2.027 2.027 2.7027
a4=2.02703 1.3514 1.3514 1.3514 1.3514 1.3514 1.3514 2.027 2.027 2.027 2.7027 2.7027 3.3784
a5=2.7027 2.027 2.027 2.027 2.027 2.027 2.027 2.7027 2.7027 2.7027 3.3784 3.3784 4.0541
a6=3.37838 2.7027 2.7027 2.7027 2.7027 2.7027 2.7027 3.3784 3.3784 3.3784 4.0541 4.0541 4.7297
a7=4.05405 3.3784 3.3784 3.3784 3.3784 3.3784 3.3784 4.0541 4.0541 4.0541 4.7297 4.7297 5.4054
a8=4.72973 4.0541 4.0541 4.0541 4.0541 4.0541 4.0541 4.7297 4.7297 4.7297 5.4054 5.4054 6.0811
a9=5.40541 4.7297 4.7297 4.7297 4.7297 4.7297 4.7297 5.4054 5.4054 5.4054 6.0811 6.0811 6.7568
a10=6.08108 5.4054 5.4054 5.4054 5.4054 5.4054 5.4054 6.0811 6.0811 6.0811 6.7568 6.7568 7.4324
a11=6.75676 5.4054 6.0811 6.0811 6.0811 6.0811 6.0811 6.7568 6.7568 6.7568 7.4324 7.4324 8.1081
a12=7.43243 6.0811 6.0811 6.7568 6.7568 6.7568 6.7568 7.4324 7.4324 7.4324 7.4324 8.1081 8.1081
a13=8.10811 6.7568 6.7568 6.7568 7.4324 7.4324 7.4324 7.4324 8.1081 8.1081 8.1081 8.7838 8.7838
a14=8.78378 7.4324 7.4324 7.4324 7.4324 8.1081 8.1081 8.1081 8.7838 8.7838 8.7838 9.4595 9.4595
a15=9.45946 8.1081 8.1081 8.1081 8.1081 8.7838 8.7838 8.7838 9.4595 9.4595 9.4595 10.135 10.135
a16=10.1351 8.7838 8.7838 8.7838 8.7838 8.7838 9.4595 9.4595 10.135 10.135 10.135 10.811 10.811
a17=10.8108 9.4595 9.4595 9.4595 9.4595 9.4595 10.135 10.135 10.811 10.811 10.811 11.486 11.486
a18=11.4865 10.135 10.135 10.135 10.135 10.135 10.811 10.811 11.486 11.486 11.486 12.162 12.162
a19=12.1622 10.811 10.811 10.811 10.811 10.811 10.811 11.486 11.486 12.162 12.162 12.838 12.838
a20=12.8378 11.486 11.486 11.486 11.486 11.486 11.486 12.162 12.162 12.838 12.838 13.514 13.514
a21=13.5135 12.162 12.162 12.162 12.162 12.162 12.162 12.838 12.838 13.514 13.514 14.189 14.189
a22=14.1892 12.838 12.838 12.838 12.838 12.838 12.838 13.514 13.514 14.189 14.189 14.865 14.865
a23=14.8649 13.514 13.514 13.514 13.514 13.514 13.514 14.189 14.189 14.865 14.865 14.865 15.541
a24=15.5405 14.189 14.189 14.189 14.189 14.189 14.189 14.865 14.865 15.541 15.541 15.541 16.216
a25=16.2162 14.865 14.865 14.865 14.865 14.865 14.865 15.541 15.541 16.216 16.216 16.216 16.892
a26=16.8919 15.541 15.541 15.541 15.541 15.541 15.541 16.216 16.216 16.892 16.892 16.892 17.568
a27=17.5676 16.216 16.216 16.216 16.216 16.216 16.216 16.892 16.892 16.892 17.568 17.568 18.243
a28=18.2432 16.892 16.892 16.892 16.892 16.892 16.892 17.568 17.568 17.568 18.243 18.243 18.919
a29=18.9189 17.568 17.568 17.568 17.568 17.568 17.568 18.243 18.243 18.243 18.919 18.919 19.595
a30=19.5946 18.243 18.243 18.243 18.243 18.243 18.243 18.919 18.919 18.919 19.595 19.595 20.27
a31=20.2703 18.919 18.919 18.919 18.919 18.919 18.919 19.595 19.595 19.595 20.27 20.27 20.946
a32=20.9459 18.919 19.595 19.595 19.595 19.595 19.595 20.27 20.27 20.27 20.946 20.946 21.622
a33=21.6216 19.595 20.27 20.27 20.27 20.27 20.27 20.946 20.946 20.946 21.622 21.622 22.297
a34=22.2973 20.27 20.27 20.946 20.946 20.946 20.946 21.622 21.622 21.622 22.297 22.297 22.973
a35=22.973 20.946 20.946 21.622 21.622 21.622 21.622 22.297 22.297 22.297 22.973 22.973 23.649
a36=23.6486 21.622 21.622 21.622 22.297 22.297 22.297 22.973 22.973 22.973 23.649 23.649 24.324
a37=24.3243 22.297 22.297 22.297 22.973 22.973 22.973 23.649 23.649 23.649 24.324 24.324 25
a38=25 22.973 22.973 22.973 22.973 23.649 23.649 24.324 24.324 24.324 25 25 25.676
a39=25.6757 23.649 23.649 23.649 23.649 24.324 24.324 24.324 25 25 25 25.676 25.676
a40=26.3514 24.324 24.324 24.324 24.324 25 25 25 25.676 25.676 25.676 26.351 26.351
a41=27.027 25 25 25 25 25.676 25.676 25.676 26.351 26.351 26.351 27.027 27.027
a42=27.7027 25.676 25.676 25.676 25.676 25.676 26.351 26.351 27.027 27.027 27.027 27.703 27.703
a43=28.3784 26.351 26.351 26.351 26.351 26.351 27.027 27.027 27.703 27.703 27.703 28.378 28.378
a44=29.0541 27.027 27.027 27.027 27.027 27.027 27.703 27.703 28.378 28.378 28.378 29.054 29.054
a45=29.7297 27.703 27.703 27.703 27.703 27.703 27.703 28.378 29.054 29.054 29.054 29.73 29.73
a46=30.4054 28.378 28.378 28.378 28.378 28.378 28.378 29.054 29.73 29.73 29.73 30.405 30.405
a47=31.0811 29.054 29.054 29.054 29.054 29.054 29.054 29.73 29.73 30.405 30.405 31.081 31.081
a48=31.7568 29.73 29.73 29.73 29.73 29.73 29.73 30.405 30.405 31.081 31.081 31.757 31.757
a49=32.4324 30.405 30.405 30.405 30.405 30.405 30.405 31.081 31.081 31.757 31.757 32.432 32.432
a50=33.1081 31.081 31.081 31.081 31.081 31.081 31.081 31.757 31.757 32.432 32.432 33.108 33.108
a51=33.7838 31.757 31.757 31.757 31.757 31.757 31.757 32.432 32.432 33.108 33.108 33.784 33.784
a52=34.4595 32.432 32.432 32.432 32.432 32.432 32.432 33.108 33.108 33.784 33.784 34.459 34.459
a53=35.1351 33.108 33.108 33.108 33.108 33.108 33.108 33.784 33.784 34.459 34.459 34.459 35.135
a54=35.8108 33.784 33.784 33.784 33.784 33.784 33.784 34.459 34.459 35.135 35.135 35.135 35.811
a55=36.4865 34.459 34.459 34.459 34.459 34.459 34.459 35.135 35.135 35.811 35.811 35.811 36.486
a56=37.1622 35.135 35.135 35.135 35.135 35.135 35.135 35.811 35.811 36.486 36.486 36.486 37.162
a57=37.8378 35.811 35.811 35.811 35.811 35.811 35.811 36.486 36.486 37.162 37.162 37.162 37.838
a58=38.5135 36.486 36.486 36.486 36.486 36.486 36.486 37.162 37.162 37.162 37.838 37.838 38.514
a59=39.1892 37.162 37.162 37.162 37.162 37.162 37.162 37.838 37.838 37.838 38.514 38.514 39.189
a60=39.8649 37.838 37.838 37.838 37.838 37.838 37.838 38.514 38.514 38.514 39.189 39.189 39.865
a61=40.5405 38.514 38.514 38.514 38.514 38.514 38.514 39.189 39.189 39.189 39.865 39.865 40.541
a62=41.2162 38.514 39.189 39.189 39.189 39.189 39.189 39.865 39.865 39.865 40.541 40.541 41.216
a63=41.8919 39.189 39.865 39.865 39.865 39.865 39.865 40.541 40.541 40.541 41.216 41.216 41.892
a64=42.5676 39.865 39.865 40.541 40.541 40.541 40.541 41.216 41.216 41.216 41.892 41.892 42.568
a65=43.2432 40.541 40.541 41.216 41.216 41.216 41.216 41.892 41.892 41.892 42.568 42.568 43.243
a66=43.9189 41.216 41.216 41.892 41.892 41.892 41.892 42.568 42.568 42.568 43.243 43.243 43.919
a67=44.5946 41.892 41.892 41.892 42.568 42.568 42.568 43.243 43.243 43.243 43.919 43.919 44.595
a68=45.2703 42.568 42.568 42.568 43.243 43.243 43.243 43.919 43.919 43.919 44.595 44.595 45.27
a69=45.9459 43.243 43.243 43.243 43.919 43.919 43.919 44.595 44.595 44.595 45.27 45.27 45.946
a70=46.6216 43.919 43.919 43.919 43.919 44.595 44.595 45.27 45.27 45.27 45.946 45.946 46.622
a71=47.2973 44.595 44.595 44.595 44.595 45.27 45.27 45.27 45.946 45.946 45.946 46.622 47.297
a72=47.973 45.27 45.27 45.27 45.27 45.946 45.946 45.946 46.622 46.622 46.622 47.297 47.297
a73=48.6486 45.946 45.946 45.946 45.946 45.946 46.622 46.622 47.297 47.297 47.297 47.973 47.973
a74=49.3243 46.622 46.622 46.622 46.622 46.622 47.297 47.297 47.973 47.973 47.973 48.649 48.649
a75=50 47.297 47.297 47.297 47.297 47.297 47.973 47.973 48.649 48.649 48.649 49.324 49.324
end
ans =
Map with properties:
Count: 11
KeyType: char
ValueType: any