def test_naax(): # todo check why for some of the large ages the test fails
i = 2
g = 0
m = 1
# this works with almost all ages and fails with some other, e.g. fails with 116
x = 121
n = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
a_grf = annuities.naax(mt=mt_GRF95, x=x, n=n, i=i, g=g, m=m, method=method)
a_tv = annuities.naax(mt=mt_TV7377, x=x, n=n, i=i, g=g, m=m, method=method)
a_grf_2 = cf_grf95.naax(x=x, m=m, n=n)
a_tv_2 = cf_tv7377.naax(x=x, m=m, n=n)
assert a_grf == pytest.approx(a_grf_2, rel=1e-16)
assert a_tv == pytest.approx(a_tv_2, rel=1e-16)
def test_nAx_():
i = 2
g = 0
n = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
ages = range(0, max(mt_TV7377.w, mt_GRF95.w) + 10)
a_grf = [
mortality_insurance.nAx_(mt=mt_GRF95,
x=x,
n=n,
i=i,
g=g,
method=method) for x in ages
]
a_tv = [
mortality_insurance.nAx_(mt=mt_TV7377,
x=x,
n=n,
i=i,
g=g,
method=method) for x in ages
]
a_grf_2 = [cf_grf95.nAx_(x=x, n=n) for x in ages]
a_tv_2 = [cf_tv7377.nAx_(x=x, n=n) for x in ages]
for idx_a, a in enumerate(a_grf):
assert (idx_a, a_grf[idx_a]) == pytest.approx((idx_a, a_grf_2[idx_a]),
rel=1e-16)
for idx_a, a in enumerate(a_tv):
assert (idx_a, a_tv[idx_a]) == pytest.approx((idx_a, a_tv_2[idx_a]),
rel=1e-16)
def test_ax():
i = 2
g = 0
m = 1
x = 200
n = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
a_grf = annuities.ax(mt=mt_GRF95, x=x, i=i, g=g, m=m, method=method)
a_tv = annuities.ax(mt=mt_TV7377, x=x, i=i, g=g, m=m, method=method)
a_grf_2 = cf_grf95.ax(x=x, m=m)
a_tv_2 = cf_tv7377.ax(x=x, m=m)
assert a_grf == pytest.approx(0, rel=1e-16)
assert a_tv == pytest.approx(0, rel=1e-16)
assert a_grf == pytest.approx(a_grf_2, rel=1e-16)
assert a_tv == pytest.approx(a_tv_2, rel=1e-16)
def test_t_ax():
i = 2
g = 1
m = 1
defer = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
ages = range(0, max(mt_TV7377.w, mt_GRF95.w) + 10)
a_grf = [
annuities.t_ax(mt=mt_GRF95,
x=x,
i=i,
g=g,
m=m,
defer=defer,
method=method) for x in ages
]
a_tv = [
annuities.t_ax(mt=mt_TV7377,
x=x,
i=i,
g=g,
m=m,
defer=defer,
method=method) for x in ages
]
a_grf_2 = [cf_grf95.t_ax(x=x, m=m, defer=defer) for x in ages]
a_tv_2 = [cf_tv7377.t_ax(x=x, m=m, defer=defer) for x in ages]
assert a_grf == pytest.approx(a_grf_2, rel=1e-16)
assert a_tv == pytest.approx(a_tv_2, rel=1e-16)
def test_t_nax():
i = 2
g = 1
m = 1
x = 45
defer = 10
n = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
a_grf = annuities.t_nax(mt=mt_GRF95,
x=x,
n=n,
i=i,
g=g,
m=m,
defer=defer,
method=method)
a_tv = annuities.t_nax(mt=mt_TV7377,
x=x,
n=n,
i=i,
g=g,
m=m,
defer=defer,
method=method)
a_grf_2 = cf_grf95.t_nax(x=x, n=n, m=m, defer=defer)
a_tv_2 = cf_tv7377.t_nax(x=x, n=n, m=m, defer=defer)
assert a_grf == pytest.approx(a_grf_2, rel=1e-16)
assert a_tv == pytest.approx(a_tv_2, rel=1e-16)
def test_t_naax(): # todo check why for some of the large ages the test fails
i = 2
g = 0
m = 1
x = 111
defer = 10
n = 5
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i,
g=g,
mt=soa_TV7377.table_qx)
a_grf = annuities.t_naax(mt=mt_GRF95,
x=x,
n=n,
i=i,
g=g,
m=m,
defer=defer,
method=method)
a_tv = annuities.t_naax(mt=mt_TV7377,
x=x,
n=n,
i=i,
g=g,
m=m,
defer=defer,
method=method)
a_grf_2 = cf_grf95.t_naax(x=x, n=n, m=m, defer=defer)
a_tv_2 = cf_tv7377.t_naax(x=x, n=n, m=m, defer=defer)
assert a_grf == pytest.approx(a_grf_2, rel=1e-16)
assert a_tv == pytest.approx(a_tv_2, rel=1e-16)
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))
'''
annuities
'''
x_s = range(20, 80 + 20, 20)
rendas_dict = {}
for x in x_s:
for m in [1, 4]:
ts = np.arange(0, lt.w - x + 1 / m, 1 / m)
v = 1 / (1 + interest_rate / 100)
this_py = os.path.split(sys.argv[0])[-1][:-3]
def parse_table_name(name):
return name.replace(' ', '').replace('/', '')
table_names = ['TV7377', 'GRF95', 'GRM95']
interest_rate = 6
mt_lst = [
rst.SoaTable('../../soa_tables/' + name + '.xml') for name in table_names
]
lt_lst = [mortality_table.MortalityTable(mt=mt.table_qx) for mt in mt_lst]
ct_lst = [
commutation_table.CommutationFunctions(i=interest_rate,
g=0,
mt=mt.table_qx) for mt in mt_lst
]
ages = np.linspace(start=20, stop=40, num=5, dtype=int)
'''
Prepare the solution for Equal Instalments
'''
capital = 100000
terms = 25
ac = annuities_certain.Annuities_Certain(interest_rate=interest_rate,
frequency=1)
ac_certain = ac.annuity_immediate(terms=terms)
equal_instalments_dict = {
'table': [],
'x': [],
'annuity_certain': [],
import pandas as pd
from soa_tables import read_soa_table_xml as rst
from essential_life import mortality_table, commutation_table
import matplotlib.pyplot as plt
table_names = ['TV7377', 'GRF95', 'GRM95']
interest_rate = 4
name = table_names[0]
mt = rst.SoaTable('../../soa_tables/' + name + '.xml')
lt = mortality_table.MortalityTable(mt=mt.table_qx)
ct = commutation_table.CommutationFunctions(i=interest_rate,
g=0,
mt=mt.table_qx)
lx = 1000
frequency = 1
first_instalment_at = 5
number_of_instalments = 1000
premium_instalments = 5
instalment = 10000
dict_annuity = {'x': 50, 'n': 1000, 'm': 1, 'defer': first_instalment_at}
renda_premium = ct.naax(x=dict_annuity['x'], n=premium_instalments)
full_liability = ct.t_naax(x=dict_annuity['x'], n=dict_annuity['n'], m=dict_annuity['m'], defer=dict_annuity['defer']) * \
instalment * lx
premium1 = full_liability / lx / renda_premium
i = interest_rate / 100
dict_liability = {
't': [],
'x': [],
import matplotlib.pyplot as plt
this_py = os.path.split(sys.argv[0])[-1][:-3]
def parse_table_name(name):
return name.replace(' ', '').replace('/', '')
table_names = ['TV7377', 'GRF95', 'GRM95']
mt_lst = [
rst.SoaTable('../../soa_tables/' + name + '.xml') for name in table_names
]
lt_lst = [mortality_table.MortalityTable(mt=mt.table_qx) for mt in mt_lst]
ct_lst = [
commutation_table.CommutationFunctions(i=4, g=0, mt=mt.table_qx)
for mt in mt_lst
]
for idx, lt in enumerate(lt_lst):
name = parse_table_name(mt_lst[idx].name)
lt.df_life_table().to_excel(excel_writer=name + '.xlsx',
sheet_name=name,
index=False,
freeze_panes=(1, 1))
ct_lst[idx].df_commutation_table().to_excel(excel_writer=name + '_comm' +
'.xlsx',
sheet_name=name,
index=False,
freeze_panes=(1, 1))
'''
__author__ = "PedroCR"
from soa_tables import read_soa_table_xml as rst
from toDelete.mortality_tables_old import TV7377, GRF95
from essential_life import mortality_insurance, mortality_table as mt, mortality_table, commutation_table
lt_tv7377 = mortality_table.MortalityTable(mt=TV7377)
lt_grf95 = mortality_table.MortalityTable(mt=GRF95)
soa_TV7377 = rst.SoaTable('../soa_tables/TV7377.xml')
soa_GRF95 = rst.SoaTable('../soa_tables/GRF95.xml')
mt_GRF95 = mt.MortalityTable(mt=soa_GRF95.table_qx)
mt_TV7377 = mt.MortalityTable(mt=soa_TV7377.table_qx)
i = 2
x = 45
inc = 1
method = 'udd'
cf_grf95 = commutation_table.CommutationFunctions(i=i, g=0, mt=soa_GRF95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=i, g=0, mt=soa_TV7377.table_qx)
a_grf = mortality_insurance.IA_x(mt=mt_GRF95, x=x, x_first=46, x_last=50, i=i, inc=inc, method=method)
a_grf = mortality_insurance.IA_x(mt=mt_TV7377, x=x, x_first=46, x_last=50, i=i, inc=inc, method=method)
a_grf_2 = cf_grf95.IAx(x=x)
cf_tv_2 = cf_tv7377.IAx(x=x)
# author: PedroCR #
from soa_tables import read_soa_table_xml as rst
from essential_life import mortality_table, commutation_table
mt_TV7377 = rst.SoaTable('../soa_tables/TV7377.xml')
mt_GRF95 = rst.SoaTable('../soa_tables/GRF95.xml')
mt_GRM95 = rst.SoaTable('../soa_tables/GRM95.xml')
lt_tv7377 = mortality_table.MortalityTable(mt=mt_TV7377.table_qx)
lt_gRF95 = mortality_table.MortalityTable(mt=mt_GRF95.table_qx)
lt_gRM95 = mortality_table.MortalityTable(mt=mt_GRM95.table_qx)
cf_tv7377 = commutation_table.CommutationFunctions(i=1.4,
g=1,
mt=mt_TV7377.table_qx)
cf_grf95 = commutation_table.CommutationFunctions(i=1.4,
g=1,
mt=mt_GRF95.table_qx)
cf_grm95 = commutation_table.CommutationFunctions(i=1.4,
g=1,
mt=mt_GRM95.table_qx)
print(cf_tv7377.df_commutation_table())
print(cf_tv7377.t_aax(55, m=1, defer=(67 - 55)))
print(cf_grm95.t_aax(55, m=1, defer=(67 - 55)))
print(cf_grf95.t_aax(55, m=1, defer=(67 - 55)))
# author: PedroCR #
from toDelete.mortality_tables_old import TV7377, GKM95_lx_15
from essential_life import mortality_table, commutation_table
lt_tv7377 = mortality_table.MortalityTable(mt=TV7377)
lt_gkm95 = mortality_table.MortalityTable(data_type='l', mt=GKM95_lx_15)
cf_tv7377 = commutation_table.CommutationFunctions(i=2, g=1.5, mt=TV7377)
print(cf_tv7377.df_commutation_table())
# test to probabilities
p = lt_gkm95.tpx(x=50, t=5)
q = lt_gkm95.tqx(x=50, t=5)
print(p)
print(q)
print(p + q)
print(lt_gkm95.msn)
print(lt_gkm95.lx_udd(25.5))
print(lt_gkm95.lx_cfm(25.5))
print(lt_gkm95.lx_bal(25.5))
print(lt_gkm95.t_nqx(x=25.5, t=5.2, n=2.3, method='cfm'))
print(lt_gkm95.msn)
print('Insurances')
print(cf_tv7377.nEx(30, 350))
print(cf_tv7377.Ax(cf_tv7377.w), '=', cf_tv7377.msn[-1])
print(cf_tv7377.Ax(150), '=', cf_tv7377.msn[-1])
print(cf_tv7377.Ax_(30), '=', cf_tv7377.msn[-1])
this_py = os.path.split(sys.argv[0])[-1][:-3]
def parse_table_name(name):
return name.replace(' ', '').replace('/', '')
table_names = ['TV7377', 'GRF95', 'GRM95']
mt_lst = [
rst.SoaTable('../../../soa_tables/' + name + '.xml')
for name in table_names
]
lt_lst = [mortality_table.MortalityTable(mt=mt.table_qx) for mt in mt_lst]
ct_lst = [
commutation_table.CommutationFunctions(i=1.4, g=1, mt=mt.table_qx)
for mt in mt_lst
]
'''
Exercises
'''
mt = lt_lst[0]
a = mt.tqx(x=52.4, t=0.2, method='udd')
print(a)
b = mt.tqx(x=52.4, t=0.2, method='cfm')
print(b)
c = mt.tpx(x=52.4, t=5.7, method='udd')
print(c)
d = mt.tpx(x=52.4, t=5.7, method='cfm')
print(d)
e = mt.t_nqx(x=52.4, t=3.2, n=2.5, method='udd')
import pytest
from soa_tables import read_soa_table_xml as rst
from essential_life import mortality_table, commutation_table
table_names = ['TV7377', 'GRF95', 'GRM95']
mt_lst = [rst.SoaTable('../../../soa_tables/' + name + '.xml') for name in table_names]
lt_lst = [mortality_table.MortalityTable(mt=mt.table_qx) for mt in mt_lst]
ct_lst = [commutation_table.CommutationFunctions(i=4, g=0, mt=mt.table_qx) for mt in mt_lst]
def test_wlai_1():
a = ct_lst[0].t_aax(x=55, m=1, defer=10)
b = ct_lst[0].t_ax(x=55, m=1, defer=9)
assert 7.774902297975 == pytest.approx(a, rel=1e-12)
assert 7.774902297975 == pytest.approx(b, rel=1e-12)
def test_wlai_2():
a = ct_lst[1].t_aax(x=55, m=1, defer=10)
b = ct_lst[1].t_ax(x=55, m=1, defer=9)
assert 10.683798089358 == pytest.approx(a, rel=1e-12)
assert 10.683798089358 == pytest.approx(b, rel=1e-12)
def test_wlai_3():
a = ct_lst[2].t_aax(x=55, m=1, defer=10)
b = ct_lst[2].t_ax(x=55, m=1, defer=9)
assert 8.365856975602 == pytest.approx(a, rel=1e-12)
assert 8.365856975602 == pytest.approx(b, rel=1e-12)
