LifeTable¶

Commutation functions and actuarial notations

The LifeTable Space provides commutation functions and actuarial notations, such as \(D_{x}\) and \(\require{enclose}{}_{f|}\overline{A}_{x}\). Mortality tables are read from input.xlsx into an ExcelRange object. The ExcelRange object is bound to a Reference, MortalityTable.

This Space is included in:

Parameters

LifeTable Space is parameterized with Sex, IntRate and TableID:

>>> simplelife.LifeTable.parameters
('Sex', 'IntRate', 'TableID')

Each ItemSpace represents commutations functions actuarial notations for a combination of Sex, IntRate and TableID. For example, LifeTable['M', 0.03, 1] contains commutation functions and actuarial notations for Male, the interest rate of 3%, mortality table 1.

Sex¶

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

Type: str

IntRate¶

The constant interest rate for discounting.

Type: float

TableID¶

The identifier of the mortality table

Type: int

References

MortalityTable¶: ExcelRange object holding mortality tables. The data is read from MortalityTables range in input.xlsx.

Example

An example of LifeTable in the simplelife model:

>>> simplelife.LifeTable['M', 0.03, 1].AnnDuenx(40, 10)
8.725179890621531

External Links:

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.