def test_tai_20_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=20,
interest_rate=5,
age_first_instalment=20 + 1,
terms=10,
fraction=1,
w=130)
assert 7.711382730455226 == pytest.approx(a, rel=1e-12)
def test_wlai_40_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=40,
interest_rate=5,
age_first_instalment=40 + 1,
terms=np.inf,
fraction=1,
w=130)
assert 17.457756571743005 == pytest.approx(a, rel=1e-12)
def test_tai_20_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=20,
interest_rate=5,
age_first_instalment=20 + 1 / 4,
terms=10,
fraction=4,
w=130)
assert 7.855310570588442 == pytest.approx(a, rel=1e-12)
def test_tad_40_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=40,
interest_rate=5,
age_first_instalment=40,
terms=10,
fraction=1,
w=130)
assert 8.086328661846537 == pytest.approx(a, rel=1e-12)
def test_wlai_40_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=40,
interest_rate=5,
age_first_instalment=40 + 1 / 4,
terms=np.inf,
fraction=4,
w=130)
assert 17.828905180633175 == pytest.approx(a, rel=1e-12)
def test_tai_80_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=80,
interest_rate=5,
age_first_instalment=80 + 1,
terms=10,
fraction=1,
w=130)
assert 6.1280362723202835 == pytest.approx(a, rel=1e-12)
def test_wlai_20_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=20,
interest_rate=5,
age_first_instalment=20 + 1 / 4,
terms=np.inf,
fraction=4,
w=130)
assert 19.337562859204613 == pytest.approx(a, rel=1e-12)
def test_tai_60_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=60,
interest_rate=5,
age_first_instalment=60 + 1 / 4,
terms=10,
fraction=4,
w=130)
assert 7.690789257141573 == pytest.approx(a, rel=1e-12)
def test_tad_80_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=80,
interest_rate=5,
age_first_instalment=80,
terms=10,
fraction=4,
w=130)
assert 6.538535827831598 == pytest.approx(a, rel=1e-12)
def test_tad_60_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=60,
interest_rate=5,
age_first_instalment=60,
terms=10,
fraction=4,
w=130)
assert 7.796128394417279 == pytest.approx(a, rel=1e-12)
def test_tai_60_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=60,
interest_rate=5,
age_first_instalment=60 + 1,
terms=10,
fraction=1,
w=130)
assert 7.534191594775955 == pytest.approx(a, rel=1e-12)
def test_tai_80_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=80,
interest_rate=5,
age_first_instalment=80 + 1 / 4,
terms=10,
fraction=4,
w=130)
assert 6.373414695745405 == pytest.approx(a, rel=1e-12)
def test_tai_40_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=40,
interest_rate=5,
age_first_instalment=40 + 1 / 4,
terms=10,
fraction=4,
w=130)
assert 7.840607131213686 == pytest.approx(a, rel=1e-12)
def test_wlad_20_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=20,
interest_rate=5,
age_first_instalment=20,
terms=np.inf,
fraction=1,
w=130)
assert 19.966393800426772 == pytest.approx(a, rel=1e-12)
def test_wlai_80_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=80,
interest_rate=5,
age_first_instalment=80 + 1 / 4,
terms=np.inf,
fraction=4,
w=130)
assert 7.917147603528528 == pytest.approx(a, rel=1e-12)
def test_tad_20_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=20,
interest_rate=5,
age_first_instalment=20,
terms=10,
fraction=4,
w=130)
assert 7.952250811733334 == pytest.approx(a, rel=1e-12)
def test_wlai_80_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=80,
interest_rate=5,
age_first_instalment=80 + 1,
terms=np.inf,
fraction=1,
w=130)
assert 7.548405606430032 == pytest.approx(a, rel=1e-12)
def test_wlai_60_4term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=60,
interest_rate=5,
age_first_instalment=60 + 1 / 4,
terms=np.inf,
fraction=4,
w=130)
assert 14.275011062804799 == pytest.approx(a, rel=1e-12)
def test_wlad_60_1term():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.annuity(x=60,
interest_rate=5,
age_first_instalment=60,
terms=np.inf,
fraction=1,
w=130)
assert 14.904074300627276 == pytest.approx(a, rel=1e-12)
def test_life_insurance_129_1frac():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
a = mml.life_insurance(x=129,
interest_rate=5,
age_first_instalment=129,
terms=np.inf,
fraction=1,
w=129)
q_w = 1 - mml.S(x=129, t=1)
assert 1 / (1 + .05) == pytest.approx(a, rel=1e-12)
def test_life_insurance_20_12frac_c():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 20 + 2 / 12
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=12,
w=129)
assert 0.05069999821147594 == pytest.approx(a, rel=1e-12)
def test_life_insurance_50_12frac_b():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 50 + 1 / 12
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=12,
w=129)
assert 0.19428541530458865 == pytest.approx(a, rel=1e-12)
def test_term_life_insurance_100_12frac():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 100
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=12,
w=129)
assert 0.8915840217595198 == pytest.approx(a, rel=1e-12)
def test_term_life_insurance_60_12frac():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 60
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=12,
w=129)
assert 0.29683037981657273 == pytest.approx(a, rel=1e-12)
def test_term_life_insurance_80_1frac():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 80
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=1,
w=129)
assert 0.592933066360474 == pytest.approx(a, rel=1e-12)
def test_life_insurance_129_12frac_b():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 129 + 11 / 12
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=12,
w=129)
assert 1.05**(-1 / 12) == pytest.approx(a, rel=1e-12)
def test_term2_life_insurance_20_1frac():
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
x0 = 20
a = mml.life_insurance(x=x0,
interest_rate=5,
age_first_instalment=x0,
terms=np.inf,
fraction=1,
w=129)
assert 0.04921934283681906 == pytest.approx(a, rel=1e-12)
from exercisesLifeContingencies.survivalModels.someMortalityLaws import makeham_mortality_functions
import scipy.integrate
mml = makeham_mortality_functions.Makeham(a=0.0001, b=0.00030, c=1.075)
'''
$\ax**[]{25:30}$
'''
i = 5
v = 1 / (1 + i / 100)
x = 25
y = 30
w = 130
prob_discount = [
mml.S(x=x, t=t) * mml.S(x=y, t=t) * v**t for t in range(w - max(x, y) + 1)
]
print('annuity:', sum(prob_discount))
'''
$\ax**[]{\overline{25:30}}$
'''
prob_discount_2 = [
(mml.S(x=x, t=t) + mml.S(x=y, t=t) - mml.S(x=x, t=t) * mml.S(x=y, t=t)) *
v**t for t in range(w - max(x, y) + 1)
]
print('annuity:', sum(prob_discount_2))
'''
$\ax**[]{25|30}=\ax**[]{30}-\ax**[]{25:30}$
'''
prob_discount_3 = [mml.S(x=y, t=t) * v**t for t in range(w - max(x, y) + 1)]
print('annuity:', sum(prob_discount_3) - sum(prob_discount))
from exercisesLifeContingencies.survivalModels.someMortalityLaws import makeham_mortality_functions
import numpy as np
from essential_life import mortality_table, commutation_table
import matplotlib.pyplot as plt
import os
import sys
this_py = os.path.split(sys.argv[0])[-1][:-3]
mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
t = np.linspace(0, 100, 1000 + 1)
x_s = [0, 20, 50, 80]
'''
Compute Life Table and commutation table
'''
interest_rate = 5
px = np.array([mml.S(x, t=1) for x in range(0, 130 + 1)])
qx = 1 - px
lt = mortality_table.MortalityTable(mt=list(np.append(0, qx)))
lt.df_life_table().to_excel(excel_writer='makeham' + '.xlsx',
sheet_name='makeham',
index=False,
freeze_panes=(1, 1))
ct = commutation_table.CommutationFunctions(i=interest_rate,
g=0,
mt=list(np.append(0, qx)))
ct.df_commutation_table().to_excel(excel_writer='makeham' + '_comm' + '.xlsx',
sheet_name='makeham',
index=False,
freeze_panes=(1, 1))
'''
from exercisesLifeContingencies.survivalModels.someMortalityLaws import makeham_mortality_functions
import numpy as np
from essential_life import mortality_table, commutation_table
import matplotlib.pyplot as plt
import os
import sys
this_py = os.path.split(sys.argv[0])[-1][:-3]
# mml = makeham_mortality_functions.Makeham(a=0.0001, b=0.0003, c=1.07)
# mml = makeham_mortality_functions.Makeham(a=0.00022, b=2.7E-6, c=1.124)
# mml = makeham_mortality_functions.Makeham(a=0.0001, b=0.00035, c=1.075)
mml = makeham_mortality_functions.Makeham(a=0.00018, b=1.9E-6, c=1.124)
interest_rate = 4
e0 = mml.moments_Tx()
e70 = mml.moments_Tx(x=70)
'''
Compute Life Table
'''
w = 125
px = np.array([mml.S(x, t=1) for x in range(0, w)])
qx = 1 - px
lt = mortality_table.MortalityTable(mt=list(np.append(0, qx)))
w = len(px)
ct = commutation_table.CommutationFunctions(i=interest_rate,
g=0,
mt=list(np.append(0, qx)))
'''
lt.df_life_table().to_excel(excel_writer='makeham_' + str(w) + '.xlsx', sheet_name='makeham',
index=False, freeze_panes=(1, 1))
