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close all
% Inaction Region
figure(1)
[~, pall] = solveh_new(sv, Winterp, p);
data = [sv(1 : p.na*p.nt, 1 : 2), pall(1 : p.na*p.nt, 1)];
data = data(data(:,1) <= 3, :);
n1 = numel(unique(data(:,1)));
n2 = numel(unique(data(:,2)));
surf(reshape(data(:,1), n1, n2), reshape(data(:,2), n1, n2), reshape(data(:,3), n1, n2)); colorbar
xlabel('$w$', 'Interpreter', 'Latex');
ylabel('$\theta$', 'Interpreter', 'Latex');
title('probability refinance', 'Interpreter', 'Latex');
xlim([0, 3])
state = gridmake(nodeunif(100, wmin, 3), 0.7, 2);
[v, pall, vall, Lall, thetaall] = solveh_new(state, Winterp, p);
call = zeros(size(pall));
aprimeall = zeros(size(pall));
sall = [state(:,3), 2*ones(size(state, 1), 1)];
for i = 1 : 2
cmax = bisect('savings', 1e-13, 1e5, Lall(:, i), p, amin); % c that implies a' = amin
cmin = bisect('savings', 1e-13, 1e5, Lall(:, i), p, amax); % c that implies a' = amax
call(:,i) = solve_golden('wfunc_new', cmin, cmax, [Lall(:,i), thetaall(:,i), sall(:,i)], EV, p);
[~, aprimeall(:,i)] = savings(call(:,i), Lall(:,i), p);
end
figure(2)
subplot(2, 3, 1)
plot(state(:,1), pall(:,1));
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('probability refinance', 'Interpreter', 'Latex');
subplot(2, 3, 2)
plot(state(:,1), Lall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$l$', 'Interpreter', 'Latex');
legend('refinance', 'dont refinance')
subplot(2, 3, 3)
plot(state(:,1), thetaall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$\theta^{\prime}$', 'Interpreter', 'Latex');
subplot(2, 3, 4)
plot(state(:,1), call);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$c$', 'Interpreter', 'Latex');
subplot(2, 3, 5)
plot(state(:,1), aprimeall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$a^{\prime}$', 'Interpreter', 'Latex');
subplot(2, 3, 6)
plot(state(:,1), [vall, v]);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('values', 'Interpreter', 'Latex');
legend('refinance', 'dont refinance', 'envelope')
figure(3)
state = gridmake(nodeunif(100, lmin, 3), 0.5, 1);
cmax = bisect('savings', 1e-13, 1e5, state(:,1), p, amin); % c that implies a' = amin
cmin = bisect('savings', 1e-13, 1e5, state(:,1), p, amax); % c that implies a' = amax
c = solve_golden('wfunc_new', cmin, cmax, state, EV, p);
[~, aprime] = savings(c, state, p);
subplot(1, 2, 1)
plot(state(:,1), c);
set(gca, 'ygrid', 'on')
xlabel('$l$', 'Interpreter', 'Latex');
title('$c$', 'Interpreter', 'Latex');
subplot(1, 2, 2)
plot(state(:,1), aprime);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$a^{\prime}$', 'Interpreter', 'Latex');
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