The CommTable Space#

Commutation functions and actuarial notations.

The CommTable Space provides commutation functions and actuarial notations, such as \(D_{x}\) and \(\require{enclose}{}_{f|}\overline{A}_{x}\). Mortality tables are read from the MortalityTables range in input.xlsx through mortality_tables() and indexed through mortality_rates().

Parameters and References#

This Space is parameterized with Sex, IntRate and TableID:

>>> m.CommTable.parameters
('Sex', 'IntRate', 'Table')

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

Sex#: A SexID code identifying the column in the mortality table.

IntRate#

The constant interest rate for discounting.

Type:: float

Table#: Identifier of the mortality table within mortality_tables().

References

mortality_tables#: Alias for mortality_tables().

Example

An example of CommTable:

>>> m.CommTable[SexID.M, 0.03, 1].AnnDuenx(40, 10)
8.725179890621531

External Links:

Cells Summary#

Life Table#

The underlying life-table columns — survivors, deaths, mortality probability and the per-age mortality rates selected for this Space’s sex and table.

`lx`(x)	The number of persons remaining at age `x`.
`dx`(x)	The number of persons who die between ages `x` and `x+1`
`qx`(x)	Probability that a person at age `x` will die in one year.
`mortality_rates`()	Mortality rates for the selected `Sex` and `Table`.

Commutation Columns#

The discount factor and the commutation columns \(D_x\), \(C_x\), \(M_x\) and \(N_x\) built from the life table.

`disc`()	The discount factor \(v = 1/(1 + i)\).
`Dx`(x)	The commutation column \(D_{x} = l_{x}v^{x}\).
`Cx`(x)	The commutation column \(\overline{C_x}\).
`Mx`(x)	The commutation column \(M_x\).
`Nx`(x)	The commutation column \(N_x\).

Assurances and Endowments#

Present values of whole-life and term assurances and of pure endowments.

`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.
`Exn`(x, n)	The value of an endowment on a person at age `x` payable after n years

Annuities#

Present values of temporary and lifetime annuities-due, with optional split payments and deferment.

`AnnDuenx`(x, n[, k, f])	The present value of an annuity-due.
`AnnDuex`(x, k[, f])	The present value of a lifetime annuity due.

Cells Descriptions#

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

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

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

mortality_rates()[source]#

Mortality rates for the selected Sex and Table.

Selects the column of mortality_tables() matching this Space’s Table and Sex parameters and returns the resulting per-age mortality rate Series.

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

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

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

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

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

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.

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

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

\[{}_{n}E_x\]

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