def grid_score(k, grid):
width, height = grid_dimensions(grid)
row_penalties = list(max(0, sum(row) - k) for row in grid)
col_penalties = list(max(0, sum(row[j] for row in grid) - k) for j in range(width))
grid = array(grid)
flip = flipud(grid)
r1 = range(-(width - 1), width)
r2 = range(-(height - 1), height)
dia_penalties = lambda m, dia_i: max(0, int(m.trace(dia_i)) - k)
di1_penalties = list(dia_penalties(grid, d) for d in r1)
di2_penalties = list(dia_penalties(flip, d) for d in r2)
return sum(row_penalties) + sum(col_penalties) + sum(di1_penalties) + sum(di2_penalties)
def grid_score(k, grid):
width, height = grid_dimensions(grid)
row_penalties = list(max(0, sum(row) - k) for row in grid)
col_penalties = list(
max(0,
sum(row[j] for row in grid) - k) for j in range(width))
grid = array(grid)
flip = flipud(grid)
r1 = range(-(width - 1), width)
r2 = range(-(height - 1), height)
dia_penalties = lambda m, dia_i: max(0, int(m.trace(dia_i)) - k)
di1_penalties = list(dia_penalties(grid, d) for d in r1)
di2_penalties = list(dia_penalties(flip, d) for d in r2)
return sum(row_penalties) + sum(col_penalties) + sum(di1_penalties) + sum(
di2_penalties)
def analytical_results(r_max, r_min, bailout_cost, discount_rate,
nr_of_periods, R, f_opt_bank_0):
# Analytical results:
# optimal value for period 0
opt_pi_bank = [0] * nr_of_periods
v_bank = [0] * nr_of_periods
#opt_pi_bank[0] = optimize.fmin(f_opt_bank_0, 0.5) # optimization using: Simplex method: the Nelder-Mead
opt_pi_bank[0] = optimize.minimize(f_opt_bank_0,
0.5,
method='L-BFGS-B',
bounds=[(0.0, 1.0)])['x']
v_bank[0] = -f_opt_bank_0(opt_pi_bank[0])
# bank problem in the rest of the periods, eq.(28)
f_bank = lambda x, y: -((x * (r_min + (r_max - r_min) * (1 - x)) +
(1 - x) * (bailout_cost + discount_rate * y)) /
(1 - discount_rate * x))
for k in range(1, nr_of_periods):
f_opt_bank_0 = lambda x: f_bank(x, v_bank[k - 1])
#opt_pi_bank[k] = optimize.fmin(f_opt_bank_0, 0.7)
opt_pi_bank[k] = optimize.minimize(f_opt_bank_0,
0.7,
method='L-BFGS-B',
bounds=[(0.0, 1.0)])['x']
v_bank[k] = -f_opt_bank_0(opt_pi_bank[k])
# Analytical results:
# check that analytical solutions coinside with optimal values:
pi_bank_analytical = [0] * nr_of_periods
v_bank_analytical = [0] * nr_of_periods
temp_v_vheck = [0] * nr_of_periods
pi_bank_analytical[0] = (1 - math.sqrt(1 - r_max * discount_rate /
(r_max - r_min))) / discount_rate
v_bank_analytical[0] = pi_bank_analytical[0] * R(
pi_bank_analytical[0]) / (1 - discount_rate * pi_bank_analytical[0])
for i in range(1, nr_of_periods):
pi_bank_analytical[i] = (1 - math.sqrt(
1 - discount_rate *
(r_max -
(bailout_cost + discount_rate * v_bank_analytical[i - 1]) *
(1 - discount_rate)) / (r_max - r_min))) / discount_rate
v_bank_analytical[i] = (
pi_bank_analytical[i] * R(pi_bank_analytical[i]) +
(1 - pi_bank_analytical[i]) *
(bailout_cost + discount_rate * v_bank_analytical[i - 1])) / (
1 - discount_rate * pi_bank_analytical[i])
# We want to solve for Rmax that would give the pi_bank same as pi_state in
# the last period:
temp_fun = lambda r_max: pi_bank_analytical[0] - (1 - math.sqrt(
1 - r_max * discount_rate / (r_max - r_min))) / discount_rate
res_sol_temp_fun = optimize.fsolve(temp_fun, 5)
# compare optimization results and analytical results:
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig2, bx = pyplot.subplots()
bx.plot(nr_per,
flipud(opt_pi_bank),
label='Optimization Results',
color='red',
linestyle=':')
bx.plot(nr_per,
flipud(pi_bank_analytical),
label='Analytical Results',
color='blue',
linestyle='--')
bx.set_xlabel('Number of Periods')
bx.set_ylabel('Probabilities')
bx.set_title('Optimal probabilities for the bank')
bx.legend(loc='upper left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig2 = mpld3.fig_to_html(fig2)
pyplot.savefig(
'tbtf/modelfinite/graphics/F_Optimal_Probabilities_for_the_Bank.pdf',
format='pdf')
pyplot.close(fig2)
return html_text_fig2, opt_pi_bank, pi_bank_analytical
def joint_problem(r_max, r_min, bailout_cost, deadweight_cost, discount_rate,
nr_of_periods):
# Joint problem: after each stage Bank promises pi <= pi_state, but recalculates it's value
opt_pi_bank_joint = [0] * nr_of_periods
opt_pi_state_joint = [0] * nr_of_periods
v_bank_joint = [0] * nr_of_periods
v_state_joint = [0] * nr_of_periods
# n=0
f_opt_bank_0 = lambda x: -x * (r_min + (r_max - r_min) *
(1 - x)) / (1 - discount_rate * x)
f_state_0 = lambda x: -deadweight_cost + bailout_cost + discount_rate * deadweight_cost * (
1 - x) / (1 - discount_rate * x)
#opt_pi_bank_joint[0] = optimize.fmin(f_opt_bank_0, 0.5) # optimization using: Simplex method: the Nelder-Mead
opt_pi_bank_joint[0] = optimize.minimize(f_opt_bank_0,
0.5,
method='L-BFGS-B',
bounds=[(0.0, 1.0)])['x']
opt_pi_state_joint[0] = optimize.root(f_state_0, 0.5, method='lm').x
# Bank "promises" the threshold pi in order to be saved at period n=1 even it it's optimal pi is lower:
if opt_pi_bank_joint[0] < opt_pi_state_joint[0]:
opt_pi_bank_joint[0] = opt_pi_state_joint[0]
v_bank_joint[0] = -f_opt_bank_0(opt_pi_bank_joint[0])
v_state_joint[0] = deadweight_cost * (1 - opt_pi_bank_joint[0]) / (
1 - discount_rate * opt_pi_bank_joint[0])
# Previous periods:
f_bank = lambda x, y: -((x * (r_min + (r_max - r_min) * (1 - x)) +
(1 - x) * (bailout_cost + discount_rate * y)) /
(1 - discount_rate * x))
f_state = lambda x,y: - deadweight_cost + bailout_cost + discount_rate * (bailout_cost + discount_rate * y) * \
(1 - x) / (1 - discount_rate * x)
# Options = optimset('TolFun', 1e-15):
for i in range(1, nr_of_periods):
f_opt_bank = lambda x: f_bank(x, v_bank_joint[i - 1])
f_state_opt = lambda x: f_state(x, v_state_joint[i - 1])
#opt_pi_bank_joint[i] = optimize.fmin(f_opt_bank, 0.7)
opt_pi_bank_joint[i] = optimize.minimize(f_opt_bank,
0.7,
method='L-BFGS-B',
bounds=[(0.0, 1.0)])['x']
opt_pi_state_joint[i] = optimize.root(f_state_opt, 0.5, method='lm').x
# BANKS's PROBABILITES CHANGED IF THEY ALE LOWER THAN PI_STATE AND THEN THEY ARE TAKEN FOR V's:
if opt_pi_bank_joint[i] < opt_pi_state_joint[i]:
opt_pi_bank_joint[i] = opt_pi_state_joint[i]
v_bank_joint[i] = -f_opt_bank(opt_pi_bank_joint[i])
v_state_joint[i] = (bailout_cost + discount_rate * v_state_joint[i-1]) * (1 - opt_pi_bank_joint[i]) /\
(1 - discount_rate * opt_pi_bank_joint[i])
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig10, jx = pyplot.subplots()
jx.plot(nr_per,
flipud(opt_pi_bank_joint),
label='Bank',
color='red',
linestyle=':')
jx.plot(nr_per,
flipud(opt_pi_state_joint),
label='State',
color='blue',
linestyle='--')
jx.set_xlabel('Stage of the Game')
jx.set_ylabel('Probability')
jx.set_title('Optimal probabilities in joint game')
jx.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig10 = mpld3.fig_to_html(fig10)
pyplot.savefig(
'tbtf/modelfinite/graphics/F_Optimal_Probabilities_in_Joint_Game.pdf',
format='pdf')
pyplot.close(fig10)
fig11, kx = pyplot.subplots()
kx.plot(nr_per, flipud(v_state_joint), color='red')
kx.set_title('State value in the joint game')
kx.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig11 = mpld3.fig_to_html(fig11)
pyplot.savefig('tbtf/modelfinite/graphics/F_State_Value_in_Joint_Game.pdf',
format='pdf')
pyplot.close(fig11)
return html_text_fig10, html_text_fig11
def states_problem_min_banks_prob_not_changed(bailout_cost, deadweight_cost,
discount_rate, nr_of_periods,
opt_pi_bank):
# State's problem: min if Bank's probabilitie is not changed
# Solve the equation from (20) on:
v_state_opt_min = [0] * nr_of_periods
pi_state_tresh_min = [0] * nr_of_periods
opt_pi_bank_min = opt_pi_bank
# n=0, pi=0 does not change
f_state_0 = lambda x: -deadweight_cost + bailout_cost + discount_rate * deadweight_cost * (
1 - x) / (1 - discount_rate * x)
pi_state_tresh_min[0] = optimize.root(f_state_0, 0.5, method='lm').x
v_state_opt_min[0] = deadweight_cost * (1 - opt_pi_bank_min[0]) / (
1 - discount_rate * opt_pi_bank_min[0])
# previous periods, n > 0:
f_state = lambda x,y: - deadweight_cost + bailout_cost + discount_rate * (bailout_cost + discount_rate * y) * \
(1 - x) / (1 - discount_rate * x)
n_end = 0
for i in range(1, nr_of_periods):
f_state_opt = lambda x: f_state(x, v_state_opt_min[i - 1])
pi_state_tresh_min[i] = optimize.root(f_state_opt, 0.5, method='lm').x
if min(deadweight_cost, bailout_cost +
discount_rate * v_state_opt_min[i - 1]) == deadweight_cost:
n_end = nr_of_periods - i + 1
v_state_opt_min[i] = min(deadweight_cost, bailout_cost + discount_rate * v_state_opt_min[i-1]) *\
(1 - opt_pi_bank_min[i]) / (1 - discount_rate * opt_pi_bank_min[i])
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig8, hx = pyplot.subplots()
hx.plot(nr_per,
flipud(opt_pi_bank_min),
label='Bank',
color='red',
linestyle=':')
hx.plot(nr_per,
flipud(pi_state_tresh_min),
label='State',
color='blue',
linestyle='--')
hx.set_xlabel('Stage of the Game')
hx.set_ylabel('Probability')
hx.set_title('Optimal Probabilities, State Chooses min(c,b+dv)')
hx.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig8 = mpld3.fig_to_html(fig8)
pyplot.savefig(
'tbtf/modelfinite/graphics/F_Optimal_Probabilities_State_Chooses_min(c_b_dv).pdf',
format='pdf')
pyplot.close(fig8)
fig9, ix = pyplot.subplots()
ix.plot(nr_per, flipud(v_state_opt_min), label='Value', color='red')
ix.set_xlabel('Stage of the Game')
ix.set_ylabel('Value')
ix.set_title('State value if it choses whether to save the bank')
ix.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig9 = mpld3.fig_to_html(fig9)
pyplot.savefig(
'tbtf/modelfinite/graphics/F_State_Value_if_it_choses_whether_to_save_the_Bank.pdf',
format='pdf')
pyplot.close(fig9)
return html_text_fig8, html_text_fig9
def states_problem_change_banks_pi(bailout_cost, deadweight_cost,
discount_rate, nr_of_periods, opt_pi_bank):
# State's problem: Change Bank's pi if it's less then State's pi
# solve the equation from (20) on:
v_state_opt_switch = [0] * nr_of_periods
pi_state_tresh_switch = [0] * nr_of_periods
opt_pi_bank_switch = opt_pi_bank
# n=0
f_state_0 = lambda x: -deadweight_cost + bailout_cost + discount_rate * deadweight_cost * (
1 - x) / (1 - discount_rate * x)
pi_state_tresh_switch[0] = optimize.fsolve(f_state_0, 0.5)
# Bank's "promises" the threshold pi in order to be saved at period n=1 even
# if it's optimal pi is lower:
if opt_pi_bank_switch[0] < pi_state_tresh_switch[0]:
opt_pi_bank_switch[0] = pi_state_tresh_switch[0]
v_state_opt_switch[0] = deadweight_cost * (1 - opt_pi_bank_switch[0]) / (
1 - discount_rate * opt_pi_bank_switch[0])
# previous periods
f_state = lambda x,y: - deadweight_cost + bailout_cost + discount_rate * (bailout_cost + discount_rate * y) * \
(1 - x) / (1 - discount_rate * x)
# solve for all the previous periods:
for i in range(1, nr_of_periods):
f_state_opt = lambda x: f_state(x, v_state_opt_switch[i - 1])
pi_state_tresh_switch[i] = optimize.fsolve(f_state_opt, 0.5)
# BANK's PROBABILITIES CHANGED IF THEY ALE LOWER THAN PI_STATE AND THEN THEY ARE TAKEN FOR V's:
if opt_pi_bank_switch[i] < pi_state_tresh_switch[i]:
opt_pi_bank_switch[i] = pi_state_tresh_switch[i]
v_state_opt_switch[i] = (bailout_cost + discount_rate * v_state_opt_switch[i-1]) * (1 - opt_pi_bank_switch[i])\
/ (1 - discount_rate * opt_pi_bank_switch[i])
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig6, fx = pyplot.subplots()
fx.plot(nr_per, flipud(opt_pi_bank), label='Bank', color='red')
fx.plot(nr_per,
flipud(pi_state_tresh_switch),
label='State',
color='blue',
linestyle=':')
fx.plot(nr_per,
flipud(opt_pi_bank_switch),
label='Bank Switched',
color='green',
linestyle='--')
fx.set_xlabel('Stage of the Game')
fx.set_ylabel('Probability')
fx.set_title('Optimal Probabilities')
fx.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig6 = mpld3.fig_to_html(fig6)
pyplot.savefig('tbtf/modelfinite/graphics/F_Optimal_Probabilities.pdf',
format='pdf')
pyplot.close(fig6)
fig7, gx = pyplot.subplots()
gx.plot(nr_per,
flipud(v_state_opt_switch),
label='New value (Bank switches)',
color='red',
linestyle=':')
gx.plot(nr_per,
flipud(v_state_opt_switch),
label='Old value',
color='blue',
linestyle='--')
gx.set_title('State value if Bank switches to state pi')
gx.legend(loc='lower left',
frameon=True,
fontsize='medium',
title='',
fancybox=True)
html_text_fig7 = mpld3.fig_to_html(fig7)
pyplot.savefig(
'tbtf/modelfinite/graphics/F_State_Value_if_Bank_Switches_to_State_pi.pdf',
format='pdf')
pyplot.close(fig7)
return html_text_fig6, html_text_fig7
def states_problem(bailout_cost, deadweight_cost, discount_rate, nr_of_periods,
opt_pi_bank, pi_bank_analytical):
# State's Problem
# solve the equations from (20) on:
v_state_opt = [0] * nr_of_periods
pi_state_thresh = [0] * nr_of_periods
# Period n=0
f_state_0 = lambda x: -deadweight_cost + bailout_cost + discount_rate * deadweight_cost * (
1 - x) / (1 - discount_rate * x)
pi_state_thresh[0] = optimize.fsolve(f_state_0, 0.5)
v_state_opt[0] = deadweight_cost * (1 - opt_pi_bank[0]) / (
1 - discount_rate * opt_pi_bank[0])
# analytical check:
pi_state_analytical = [0] * nr_of_periods
pi_state_analytical[0] = (
deadweight_cost -
(deadweight_cost - bailout_cost) / discount_rate) / bailout_cost
# previous periods:
f_state = lambda x,y: - deadweight_cost + bailout_cost + discount_rate * (bailout_cost + discount_rate * y) * (1 - x) /\
(1 - discount_rate * x)
# solve for the rest of the periods:
for i in range(1, nr_of_periods):
f_state_opt = lambda x: f_state(x, v_state_opt[i - 1])
pi_state_thresh[i] = optimize.fsolve(f_state_opt, 0.5)
#BANK's PROBABILITIE'sS ARE TAKEN FOR v_state
v_state_opt[i] = (
bailout_cost + discount_rate * v_state_opt[i - 1]) * (
1 - opt_pi_bank[i]) / (1 - discount_rate * opt_pi_bank[i])
pi_state_analytical[i] = (
bailout_cost + (discount_rate * v_state_opt[i - 1]) -
(deadweight_cost - bailout_cost) / discount_rate) / (
bailout_cost + (discount_rate * v_state_opt[i - 1]) -
(deadweight_cost - bailout_cost))
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig3, cx = pyplot.subplots()
cx.plot(nr_per,
flipud(opt_pi_bank),
label='Bank',
color='red',
linestyle=':')
cx.plot(nr_per,
flipud(pi_state_thresh),
label='State',
color='blue',
linestyle='--')
cx.set_xlabel('Stage of the Game')
cx.set_ylabel('Probability')
cx.set_title('Machine Results')
cx.legend(loc='upper left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig3 = mpld3.fig_to_html(fig3)
pyplot.savefig('tbtf/modelfinite/graphics/F_Machine_Results.pdf',
format='pdf')
pyplot.close(fig3)
fig4, dx = pyplot.subplots()
dx.plot(nr_per,
flipud(pi_bank_analytical),
label='Bank',
color='red',
linestyle=':')
dx.plot(nr_per,
flipud(pi_state_analytical),
label='State',
color='blue',
linestyle='--')
dx.set_xlabel('Stage of the Game')
dx.set_ylabel('Probability')
dx.set_title('Analytical Results')
dx.legend(loc='upper left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig4 = mpld3.fig_to_html(fig4)
pyplot.savefig('tbtf/modelfinite/graphics/F_Analytical_Results.pdf',
format='pdf')
pyplot.close(fig4)
fig5, ex = pyplot.subplots()
ex.plot(nr_per, flipud(v_state_opt), label='State_Value_Function')
ex.set_title('State Value Function')
html_text_fig5 = mpld3.fig_to_html(fig5)
pyplot.savefig('tbtf/modelfinite/graphics/F_State_Value_Function.pdf',
format='pdf')
pyplot.close(fig5)
return html_text_fig3, html_text_fig4, html_text_fig5, opt_pi_bank
def banks_problem_analytical_results(r_max, r_min, bailout_cost, discount_rate,
nr_of_periods, R):
# Bank's problem:
# bank's problem at the last stage: max(pi) pi*R(pi)/(1-delta*pi)
f_opt_bank_0 = lambda x: -x * (r_min + (r_max - r_min) *
(1 - x)) / (1 - discount_rate * x)
# Analytical results:
# optimal value for period 0
opt_pi_bank = [0] * nr_of_periods
v_bank = [0] * nr_of_periods
opt_pi_bank[0] = optimize.fmin(
f_opt_bank_0,
0.5) # optimization using: Simplex method: the Nelder-Mead
v_bank[0] = -f_opt_bank_0(opt_pi_bank[0])
# bank problem in the rest of the periods, eq.(28)
f_bank = lambda x, y: -((x * (r_min + (r_max - r_min) * (1 - x)) +
(1 - x) * (bailout_cost + discount_rate * y)) /
(1 - discount_rate * x))
for k in range(1, nr_of_periods):
f_opt_bank_0 = lambda x: f_bank(x, v_bank[k - 1])
opt_pi_bank[k] = optimize.fmin(f_opt_bank_0, 0.7)
v_bank[k] = -f_opt_bank_0(opt_pi_bank[k])
# Analytical results:
# check that analytical solutions coinside with optimal values:
pi_bank_analytical = [0] * nr_of_periods
v_bank_analytical = [0] * nr_of_periods
temp_v_vheck = [0] * nr_of_periods
pi_bank_analytical[0] = (1 - math.sqrt(1 - r_max * discount_rate /
(r_max - r_min))) / discount_rate
v_bank_analytical[0] = pi_bank_analytical[0] * R(
pi_bank_analytical[0]) / (1 - discount_rate * pi_bank_analytical[0])
for i in range(1, nr_of_periods):
pi_bank_analytical[i] = (1 - math.sqrt(
1 - discount_rate *
(r_max -
(bailout_cost + discount_rate * v_bank_analytical[i - 1]) *
(1 - discount_rate)) / (r_max - r_min))) / discount_rate
v_bank_analytical[i] = (
pi_bank_analytical[i] * R(pi_bank_analytical[i]) +
(1 - pi_bank_analytical[i]) *
(bailout_cost + discount_rate * v_bank_analytical[i - 1])) / (
1 - discount_rate * pi_bank_analytical[i])
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig1, ax = pyplot.subplots()
ax.plot(nr_per,
flipud(opt_pi_bank),
label='Machine Results',
color='red',
linestyle=':')
ax.plot(nr_per,
flipud(pi_bank_analytical),
label='Analytical Results',
color='blue',
linestyle='--')
ax.set_xlabel('Number of Periods')
ax.set_ylabel('Probabilities')
ax.set_title('Optimal probabilities for the bank')
ax.legend(loc='upper left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig1 = mpld3.fig_to_html(fig1)
pyplot.savefig(
'tbtf/modelfinitebounded/graphics/FB_Optimal_Probabilities_for_the_Bank.pdf',
format='pdf')
pyplot.close(fig1)
return html_text_fig1, opt_pi_bank, pi_bank_analytical
def states_problem(bailout_cost, deadweight_cost, discount_rate, nr_of_periods,
opt_pi_bank):
# State's Problem
# solve the equations from (20) on:
v_state_opt = [0] * nr_of_periods
pi_state_thresh = [0] * nr_of_periods
x = math.pow(5, 2)
# Period n=0
f_state_0 = lambda x: math.pow(
-deadweight_cost + bailout_cost + discount_rate * deadweight_cost *
(1 - x) / (1 - discount_rate * x), 2)
pi_state_thresh[0] = optimize.fsolve(f_state_0, 0.5)
v_state_opt[0] = deadweight_cost * (1 - opt_pi_bank[0]) / (
1 - discount_rate * opt_pi_bank[0])
# previous periods:
f_state = lambda x, y: math.pow(
-deadweight_cost + bailout_cost + discount_rate *
(bailout_cost + discount_rate * y) * (1 - x) /
(1 - discount_rate * x), 2)
# solve for the rest of the periods:
for i in range(1, nr_of_periods):
f_state_opt = lambda x: f_state(x, v_state_opt[i - 1])
pi_state_thresh[i] = optimize.fsolve(f_state_opt, 0.5)
#BANK's PROBABILITIE'sS ARE TAKEN FOR v_state
v_state_opt[i] = (bailout_cost + discount_rate * v_state_opt[i - 1]) * (1 - opt_pi_bank[i]) / \
(1 - discount_rate * opt_pi_bank[i])
nr_per = [0] * nr_of_periods
for i in range(0, nr_of_periods):
nr_per[i] = i
# Create plots and pdf file. Save pdf file into graphics folder
fig2, ax = pyplot.subplots()
ax.plot(nr_per,
flipud(opt_pi_bank),
label='Bank',
color='red',
linestyle=':')
ax.plot(nr_per,
flipud(pi_state_thresh),
label='State',
color='blue',
linestyle='--')
ax.set_xlabel('Stage of the Game')
ax.set_ylabel('Probability')
ax.set_title('Optimal Probabilities')
ax.legend(loc='upper left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig2 = mpld3.fig_to_html(fig2)
pyplot.savefig(
'tbtf/modelfinitebounded/graphics/FB_Optimal_Probabilities.pdf',
format='pdf')
pyplot.close(fig2)
fig3, bx = pyplot.subplots()
bx.plot(nr_per, flipud(v_state_opt), label='Bank', color='red')
bx.set_title('State Value')
bx.legend(loc='lower left',
frameon=0,
fontsize='medium',
title='',
fancybox=True)
html_text_fig3 = mpld3.fig_to_html(fig3)
pyplot.savefig('tbtf/modelfinitebounded/graphics/FB_State_Value.pdf',
format='pdf')
pyplot.close(fig3)
return html_text_fig2, html_text_fig3, v_state_opt