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.