LifeTable#

Commutation functions and actuarial notations

The LifeTable Space provides commutation functions and actuarial notations, such as $D_{x}$ and $_{f |} {\overset{―}{A}}_{x}$ . 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 $\overset{―}{C_{x}}$ .
`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.

_{f |} {\ddot{a}}_{x : 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.

$_{f |} {\overset{―}{A}}_{x}$

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.

$_{f |} {\overset{―}{A}}_{x : n}^{1}$

Cx(x)[source]#: The commutation column $\overset{―}{C_{x}}$ .

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.