LifeTable#

Commutation functions and actuarial notations

The LifeTable Space includes Cells to calculate commutation functions and actuarial notations. LifeTable is parameterized with Sex, IntRate and TableID. TableID and Sex are used in qx() below to identify the mortality rates to be applied.

Example

>>> fastlife.LifeTable['M', 0.03, 3].AnnDuenx(x=30, n=10)
8.752619688735953

>>> fastlife.LifeTable['F', 0.03, 3].qx(x=50)
0.00196

>>> fastlife.LifeTable.MortalityTables()
           1                 2                 3                 4
           M        F        M        F        M        F        M        F
0    0.00246  0.00210  0.00298  0.00252  0.00345  0.00298  0.00456  0.00383
1    0.00037  0.00033  0.00045  0.00034  0.00051  0.00044  0.00069  0.00059
2    0.00026  0.00023  0.00032  0.00025  0.00038  0.00030  0.00051  0.00041
3    0.00018  0.00015  0.00022  0.00018  0.00027  0.00020  0.00037  0.00028
4    0.00013  0.00011  0.00016  0.00013  0.00021  0.00014  0.00029  0.00021
..       ...      ...      ...      ...      ...      ...      ...      ...
126  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000
127  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000
128  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000
129  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000
130  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000

[131 rows x 8 columns]

References

Space Parameters

Sex#: ‘M’ or ‘F’ to indicate male or female column in the mortality table.

IntRate#: Constant interest rate for discounting.

TableID#: ID of an ultimate mortality table by sex and age.

References

MortalityTables#: PandasData object holding the data of mortality tables. The data is read from MortalityTables.xlsx. Defined also in fastlife.model.LifeTable, fastlife.model.Input and fastlife.model.Projection.Assumptions

Cells

`AnnDuenx`(x, n[, k, f])	The present value of an annuity-due.
`AnnDuex`(x, k[, f])	The present value of a lifetime annuity due.
`Ax`(x[, f])	The present value of a lifetime assurance on a person at age `x` payable immediately upon death, optionally with an waiting period of `f` years.
`Axn`(x, n[, f])	The present value of an assurance on a person at age `x` payable immediately upon death, optionally with an waiting period of `f` years.
`Cx`(x)	The commutation column \(\overline{C_x}\).
`Dx`(x)	The commutation column \(D_{x} = l_{x}v^{x}\).
`Exn`(x, n)	The value of an endowment on a person at age `x` payable after n years
`Mx`(x)	The commutation column \(M_x\).
`Nx`(x)	The commutation column \(N_x\).
`disc`()	The discount factor \(v = 1/(1 + i)\).
`dx`(x)	The number of persons who die between ages `x` and `x+1`
`lx`(x)	The number of persons remaining at age `x`.
`qx`(x)	Probability that a person at age `x` will die in one year.

AnnDuenx(x, n, k=1, f=0)[source]#

The present value of an annuity-due.

\[\require{enclose}{}_{f|}\ddot{a}_{x:\enclose{actuarial}{n}}^{(k)}\]

Parameters:

x (int) – age
n (int) – length of annuity payments in years
k (int, optional) – number of split payments in a year
f (int, optional) – waiting period in years

AnnDuex(x, k, f=0)[source]#

The present value of a lifetime annuity due.

Parameters:

x (int) – age
k (int, optional) – number of split payments in a year
f (int, optional) – waiting period in years

Ax(x, f=0)[source]#: The present value of a lifetime assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years.

\[\require{enclose}{}_{f|}\overline{A}_{x}\]

Axn(x, n, f=0)[source]#: The present value of an assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years.

\[\require{enclose}{}_{f|}\overline{A}^{1}_{x:\enclose{actuarial}{n}}\]

Cx(x)[source]#: The commutation column \(\overline{C_x}\).

Dx(x)[source]#: The commutation column \(D_{x} = l_{x}v^{x}\).

Exn(x, n)[source]#: The value of an endowment on a person at age x payable after n years

\[{}_{n}E_x\]

Mx(x)[source]#: The commutation column \(M_x\).

Nx(x)[source]#: The commutation column \(N_x\).

disc()[source]#: The discount factor \(v = 1/(1 + i)\).

dx(x)[source]#: The number of persons who die between ages x and x+1

lx(x)[source]#: The number of persons remaining at age x.

qx(x)[source]#: Probability that a person at age x will die in one year.