def reserves_predicted_scale_knn(x,
n,
i,
a,
m,
stress_MT=0,
stress_interest_rates=0,
adapt=True):
if adapt == True:
## First, We compute the best model
model = best_model_scale_knn(stress_MT, stress_interest_rates, X=X)
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
i = i + stress_i
listcontract = np.zeros((1, n + 1))
list_annual_premium1 = np.zeros((1, n + 1))
list_natural_premium1 = np.zeros((1, n + 1))
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i) * (1 - qx)
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium1[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * (1 / (1 + i)) * qx
listcontract[0][term] = (left - right) / down
list_natural_premium1[0][term - 1] = a * qx
recurrence1 = listcontract[0]
else:
model = best_model_scale_knn(stress_MT=0, stress_interest=0, X=X)
list_annual_premium1 = np.zeros((1, n + 1))
list_natural_premium1 = np.zeros((1, n + 1))
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((1, n + 1))
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium1[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * qx
listcontract[0][term] = (left - right) / down
list_natural_premium1[0][term] = a * qx
recurrence1 = listcontract[0]
return ([i for i in range(1, n + 2)], recurrence1, list_annual_premium1[0],
list_natural_premium1[0])
def reserves_true(x,
n,
i,
a,
m,
stress_MT=0,
stress_interest_rates=0,
adapt=True):
if adapt == True:
stress = stress_MT
stress_i = stress_interest_rates
i = i + stress_i
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((1, n + 1))
list_annual_premium2 = np.zeros((1, n + 1))
list_natural_premium2 = np.zeros((1, n + 1))
annual_premium = stresstest.TermInsuranceAnnual(x, n, i, a, m, newTH)
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i) * (1 - qx)
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium2[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * (1 / (1 + i)) * qx
list_natural_premium2[0][term - 1] = a * (1 / (1 + i)) * qx
listcontract[0][term] = (left - right) / down
recurrence2 = listcontract[0]
else:
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((1, n + 1))
annual_premium = stresstest.TermInsuranceAnnual(x, n, i, a, m, TH)
list_annual_premium2 = np.zeros((1, n + 1))
list_natural_premium2 = np.zeros((1, n + 1))
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i + stress_i) * (1 - qx)
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium2[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * (1 / (1 + i + stress_i)) * qx
list_natural_premium2[0][term - 1] = a * (1 /
(1 + i + stress_i)) * qx
listcontract[0][term] = (left - right) / down
recurrence2 = listcontract[0]
return ([i for i in range(1, n + 2)], recurrence2, list_annual_premium2[0],
list_natural_premium2[0])
def reserves_predicted_model(x,
n,
i,
a,
m,
model,
stress_MT=0,
stress_interest_rates=0,
adapt=True):
if adapt == True:
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
i = i + stress_i
listcontract = np.zeros((1, n + 1))
list_annual_premium1 = np.zeros((1, n + 1))
list_natural_premium1 = np.zeros((1, n + 1))
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i) * (1 - qx)
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium1[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * (1 / (1 + i)) * qx
listcontract[0][term] = (left - right) / down
list_natural_premium1[0][term - 1] = a * qx * (1 / (1 + i))
recurrence1 = listcontract[0]
else:
list_annual_premium1 = np.zeros((1, n + 1))
list_natural_premium1 = np.zeros((1, n + 1))
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((1, n + 1))
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i + stress_i) * (1 - qx)
if (term <= m):
left = listcontract[0][term - 1] + annual_premium
list_annual_premium1[0][term - 1] = annual_premium
else:
left = listcontract[0][term - 1]
right = a * qx * (1 / (1 + i + stress_i))
listcontract[0][term] = (left - right) / down
list_natural_premium1[0][term] = a * qx * (1 / (1 + i + stress_i))
recurrence1 = listcontract[0]
return (recurrence1, list_annual_premium1[0], list_natural_premium1[0])
def balance_sheet_true(x,
n,
i,
a,
m,
stress_MT=0,
stress_interest_rates=0,
adapt=True):
if adapt == True:
bs = reserves.reserves_true(x, n, i, a, m, stress_MT,
stress_interest_rates, adapt)
Premiums = bs[1 + 1]
Financial_income = (bs[0 + 1] + Premiums) * (i + stress_interest_rates)
Last_premium_reserves = bs[0 + 1]
Claims = bs[2 + 1] * (1 + (i + stress_interest_rates))
Premium_reserves = bs[0 + 1][1:len(bs[0 + 1])]
Premium_reserves = Premium_reserves + [0]
Total_Asset = list()
Total_liability = list()
for age in range(0, len(Premium_reserves)):
Premium_reserves[age] = Premium_reserves[age] * stresstest.NPX(
x + age, 1,
stresstest.StressTest_table(TH, stress_MT)[0])
Total_Asset.append(Financial_income[age] + Premiums[age] +
Last_premium_reserves[age])
Total_liability.append(Claims[age] + Premium_reserves[age])
else:
bs = reserves.reserves_true(x, n, i, a, m, stress_MT,
stress_interest_rates, adapt)
Premiums = bs[1 + 1]
Financial_income = (bs[0 + 1] + Premiums) * (i + stress_interest_rates)
Last_premium_reserves = bs[0 + 1]
Claims = bs[2 + 1] * (1 + (i + stress_interest_rates))
Premium_reserves = bs[0 + 1][1:len(bs[1])]
Premium_reserves = Premium_reserves + [0]
Total_Asset = list()
Total_liability = list()
for age in range(0, len(Premium_reserves)):
Premium_reserves[age] = Premium_reserves[age] * stresstest.NPX(
x + age, 1,
stresstest.StressTest_table(TH, stress_MT)[0])
Total_Asset.append(Financial_income[age] + Premiums[age] +
Last_premium_reserves[age])
Total_liability.append(Claims[age] + Premium_reserves[age])
return Premiums[0:-1], Financial_income[0:-1], Last_premium_reserves[
0:-1], Claims[0:-1], Premium_reserves, Total_Asset, Total_liability
def best_model_scale_knn(stress_MT=0, stress_interest=0, X=X):
##put the stress in %
y_stressed = list()
stress = stress_MT #/100
stress_i = stress_interest #/100
TH_stressed = stresstest.StressTest_table(TH, stress)[0]
X_new = X.copy()
X_new.interest_rate = X_new.interest_rate + stress_i
for contract in range(0, len(X)):
y_stressed.append(
stresstest.TermInsuranceAnnual(
int(X_new.iloc[contract].age),
int(X_new.iloc[contract].maturity),
X_new.iloc[contract].interest_rate,
X_new.iloc[contract].amount,
int(X_new.iloc[contract].nb_payements), TH_stressed))
X_trainval, X_test, y_trainval, y_test = train_test_split(X_new,
y_stressed,
random_state=1)
X_train, X_valid, y_train, y_valid = train_test_split(X_trainval,
y_trainval,
random_state=1)
test_scores_scaled = list()
train_scores_scaled = list()
nn_list_scaled = list()
for nn in range(7, 9):
nn_list_scaled.append(nn)
scaler = MinMaxScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
poly_scaled = PolynomialFeatures(degree=nn, include_bias=False)
poly_scaled.fit(X_train_scaled)
X_poly_train_scaled = poly_scaled.transform(X_train_scaled)
X_poly_test_scaled = poly_scaled.transform(X_test_scaled)
model = LinearRegression().fit(X_poly_train_scaled, y_train)
test_scores_scaled.append(model.score(X_poly_test_scaled, y_test))
train_scores_scaled.append(model.score(X_poly_train_scaled, y_train))
m = max(test_scores_scaled)
max_nn_scaled = 0
for nn in range(7, 9):
if test_scores_scaled[nn - 7] == m:
max_nn_scaled = nn
scaler = MinMaxScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_new)
poly_scaled = PolynomialFeatures(degree=max_nn_scaled, include_bias=False)
poly_scaled.fit(X_train_scaled)
X_poly_train_scaled = poly_scaled.transform(X_train_scaled)
X_poly_test_scaled = poly_scaled.transform(X_test_scaled)
model = LinearRegression().fit(X_poly_train_scaled, y_train)
y_poly = model.predict(X_poly_test_scaled)
y_poly = np.abs(y_poly)
##now we train knn
model = KNeighborsRegressor(n_neighbors=20, weights="distance")
model.fit(X_new, y_poly)
return model
def reserves_sum_knn(stress_MT=0, stress_interest_rates=0, adapt=True):
level_annual_premium = np.zeros((len(X), 41))
natural_premium = np.zeros((len(X), 41))
if adapt == True:
## First, We compute the best model
model = best_model_scale_knn(stress_MT, stress_interest_rates, X)
# model=stresstest. best_model_scale_knn(stress_MT,stress_interest_rates,X)[0]
stress = stress_MT #/100
stress_i = stress_interest_rates #/100
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((len(X), 41))
for contract in range(0, len(X)):
x = int(X.iloc[contract].age)
m = int(X.iloc[contract].nb_payements)
n = int(X.iloc[contract].maturity)
i = X.iloc[contract].interest_rate + stress_i
a = X.iloc[contract].amount
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i) * (1 - qx)
if (term <= m):
left = listcontract[contract][term - 1] + annual_premium
level_annual_premium[contract][term - 1] = annual_premium
else:
left = listcontract[contract][term - 1]
right = a * (1 / (1 + i)) * qx
natural_premium[contract][term - 1] = a * qx * (1 / (1 + i))
listcontract[contract][term] = (left - right) / down
recurrence2 = list()
level_annual_premium_total = list()
natural_premium_total = list()
for term in range(0, 41):
## print(np.sum(listcontract[:,40]))
recurrence2.append(np.sum(listcontract[:, term]))
natural_premium_total.append(np.sum(natural_premium[:, term]))
level_annual_premium_total.append(
np.sum(level_annual_premium[:, term]))
else:
model = best_model_scale_knn(0, 0, X)
# model=stresstest. best_model_stress(0,0,X)[0]
stress = stress_MT #/100
stress_i = stress_interest_rates #/100
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((len(X), 41))
for contract in range(0, len(X)):
x = int(X.iloc[contract].age)
m = int(X.iloc[contract].nb_payements)
n = int(X.iloc[contract].maturity)
i = X.iloc[contract].interest_rate
a = X.iloc[contract].amount
annual_premium = model.predict([[x, m, n, i, a]])
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i + stress_i) * (1 - qx)
if (term <= m):
left = listcontract[contract][term - 1] + annual_premium
level_annual_premium[contract][term - 1] = annual_premium
else:
left = listcontract[contract][term - 1]
right = a * qx * (1 / (1 + i + stress_i))
natural_premium[contract][term -
1] = a * qx * (1 /
(1 + i + stress_i))
listcontract[contract][term] = (left - right) / down
recurrence2 = list()
level_annual_premium_total = list()
natural_premium_total = list()
for term in range(0, 41):
recurrence2.append(np.sum(listcontract[:, term]))
natural_premium_total.append(np.sum(natural_premium[:, term]))
level_annual_premium_total.append(
np.sum(level_annual_premium[:, term]))
reserve_total = recurrence2
return ([i for i in range(1, 42)], reserve_total, natural_premium_total,
level_annual_premium_total)
def reserves_sum(stress_MT=0, stress_interest_rates=0, adapt=False):
#put stress in %
level_annual_premium = np.zeros((len(X), 41))
natural_premium = np.zeros((len(X), 41))
if adapt == True:
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((len(X), 41))
for contract in range(0, len(X)):
x = int(X.iloc[contract].age)
m = int(X.iloc[contract].nb_payements)
n = int(X.iloc[contract].maturity)
i = X.iloc[contract].interest_rate + stress_i
a = X.iloc[contract].amount
annual_premium = stresstest.TermInsuranceAnnual(
x, n, i, a, m, newTH)
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
natural_premium[contract][term - 1] = a * (1 / (1 + i)) * qx
down = 1 / (1 + i) * (1 - qx)
if (term <= m):
level_annual_premium[contract][term - 1] = annual_premium
left = listcontract[contract][term - 1] + annual_premium
else:
left = listcontract[contract][term - 1]
right = a * (1 / (1 + i)) * qx
listcontract[contract][term] = (left - right) / down
reserve_total = list()
level_annual_premium_total = list()
natural_premium_total = list()
for term in range(0, 41):
## print(np.sum(listcontract[:,40]))
level_annual_premium_total.append(
np.sum(level_annual_premium[:, term]))
natural_premium_total.append(np.sum(natural_premium[:, term]))
reserve_total.append(np.sum(listcontract[:, term]))
else:
stress = stress_MT
stress_i = stress_interest_rates
newTH = stresstest.StressTest_table(TH, stress)[0]
listcontract = np.zeros((len(X), 41))
for contract in range(0, len(X)):
x = int(X.iloc[contract].age)
m = int(X.iloc[contract].nb_payements)
n = int(X.iloc[contract].maturity)
i = X.iloc[contract].interest_rate
a = X.iloc[contract].amount
annual_premium = stresstest.TermInsuranceAnnual(x, n, i, a, m, TH)
for term in range(1, n + 1):
qx = stresstest.Qx(x + term - 1, newTH)
down = 1 / (1 + i + stress_i) * (1 - qx)
natural_premium[contract][term -
1] = a * (1 /
(1 + i + stress_i)) * qx
if (term <= m):
level_annual_premium[contract][term - 1] = annual_premium
left = listcontract[contract][term - 1] + annual_premium
else:
left = listcontract[contract][term - 1]
right = a * (1 / (1 + i + stress_i)) * qx
listcontract[contract][term] = (left - right) / down
reserve_total = list()
level_annual_premium_total = list()
natural_premium_total = list()
for term in range(0, 41):
level_annual_premium_total.append(
np.sum(level_annual_premium[:, term]))
natural_premium_total.append(np.sum(natural_premium[:, term]))
reserve_total.append(np.sum(listcontract[:, term]))
return ([i for i in range(1, 42)], reserve_total, natural_premium_total,
level_annual_premium_total)