lifetable¶

Source module to create LifeTable space from.

This is a source module to create LifeTable space and its sub spaces from.

This module is passed to import_module method to create a space that contains cells that defines life tables and commutation functions, for a selected combination of Sex, IntRate and MortalityTable.

MortalityTable and Sex are used in qx() below to identify the mortality rates to be applied.

Example

Sample script:

from modelx import *
space = new_model().import_module(module=lifetable)
space.Sex = 'M'
space.IntRate = 0.03
space.MortalityTable = lambda sex, x: 0.001 if x < 110 else 1

References

International actuarial notation by F.S.Perryman

Project Templates

This module is included in the following project templates.

References in Sub

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

nestedlife.lifetable.IntRate¶: The constant interest rate for discounting.

nestedlife.lifetable.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.

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

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

nestedlife.lifetable.dx(x)[source]¶: The number of persons who die between ages x and x+1

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

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

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

nestedlife.lifetable.Nx(x)[source]¶: The commutation column \(N_x\).

nestedlife.lifetable.Mx(x)[source]¶: The commutation column \(M_x\).

nestedlife.lifetable.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.

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

nestedlife.lifetable.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.

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

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

\[{}_{n}E_x\]

nestedlife.lifetable.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

nestedlife.lifetable.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