LifeTable¶

Commutation functions and actuarial notations

The LifeTable space includes Cells to calculate commutation functions and actuarial notations for given Sex, IntRate and MortalityTable. MortalityTable and Sex are used in qx() below to identify the mortality rates to be applied.

Example

An example of LifeTable in the simplelife model:

>>> space = simplelife.LifeTable

>>> space.Sex = 'M'

>>> space.IntRate = 0.03

>>> space.MortalityTable = lambda sex, x: 0.001 if x < 110 else 1

>>> space.AnnDuenx(40, 10)

References

Project Templates

This module is included in the following project templates.

References in Sub

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

IntRate¶: The constant interest rate for discounting.

MortalityTable¶: The ultimate mortality table by sex and age.

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.