selectlife

Select and Ultimate Life Table – Loads and calculates select life tables

MIT License. Copyright 2022-2023 Terence Lim

class actuarialmath.selectlife.SelectLife(periods: int = 0, udd: bool = True, verbose: bool = False, **kwargs)[source]

Bases: LifeTable

Calculate select life table, and iteratively fill in missing values

Parameters:

  • periods – number of select period years

  • verbose – whether to echo update steps

Notes

6 types of columns can be loaded and calculated in the select table:

  • ‘q’ : probability [x]+s dies in one year

  • ‘l’ : number of lives aged [x]+s

  • ‘d’ : number of deaths of age [x]+s

  • ‘A’ : whole life insurance

  • ‘a’ : whole life annuity

  • ‘e’ : expected future curtate lifetime of [x]+s

__getitem__(table: str) → Dict[int, float][source]

Returns values from a select and ultimate table

Parameters:

table – may be {‘l’, ‘q’, ‘e’, ‘d’, ‘a’, ‘A’}

set_table(l: Dict[int, List[float]] | None = None, d: Dict[int, List[float]] | None = None, q: Dict[int, List[float]] | None = None, A: Dict[int, List[float]] | None = None, a: Dict[int, List[float]] | None = None, e: Dict[int, List[float]] | None = None, fill: bool = True, radix: int = 100000) → SelectLife[source]

Update from table, every age has row for all select durations

Parameters:

  • q – probability [x]+s dies in one year

  • l – number of lives aged [x]+s

  • d – number of deaths of [x]+s

  • A – whole life insurance, or

  • a – whole life annuity, or

  • e – expected future lifetime of [x]+s

  • radix – initial number of lives

  • fill – whether to fill missing values using recursion formulas

Examples

>>> life = SelectLife().set_table(l={55: [10000, 9493, 8533, 7664],
>>>                                  56: [8547, 8028, 6889, 5630],
>>>                                  57: [7011, 6443, 5395, 3904],
>>>                                  58: [5853, 4846, 3548, 2210]},
>>>                               e={57: [None, None, None, 1]})
>>> print(life.e_r(58, s=2))
set_select(s: int, age_selected: bool, radix: int = 100000, fill: bool = False, l: Dict[int, float] | None = None, d: Dict[int, float] | None = None, q: Dict[int, float] | None = None, A: Dict[int, float] | None = None, a: Dict[int, float] | None = None, e: Dict[int, float] | None = None) → SelectLife[source]

Update a table column, for a particular duration s in the select period

Parameters:

  • s – column to populate - n is ultimate, 0..n-1 is year after select

  • age_selected – is indexed by age selected or actual (False, default)

  • radix – initial number of lives

  • fill – whether to fill missing values using recursion formulas

  • q – probabilities [x]+s dies in next year, by age

  • l – number of lives aged [x]+s, by age

  • d – number of deaths of [x]+s, by age

  • A – whole life insurance of [x]+s, by age

  • a – whole life annuity of [x]+s, by age

  • e – expected future lifetime of [x]+s, by age

fill_table(radix: int = 100000) → SelectLife[source]

Fills in missing table values (does not check for consistency)

Parameters:

radix – initial number of lives

A_x(x: int, s: int = 0, moment: int = 1, discrete: bool = True, **kwargs) → float[source]

Returns insurance value computed from select table

Parameters:

  • x – age of selection

  • s – years after selection

a_x(x: int, s: int = 0, moment: int = 1, discrete: bool = True, **kwargs) → float[source]

Returns annuity value computed from select table

Parameters:

  • x – age of selection

  • s – years after selection

l_x(x: int, s: int = 0) → float[source]

Returns number of lives aged [x]+s computed from select table

Parameters:

  • x – age of selection

  • s – years after selection

p_x(x: int, s: int = 0, t: int = 1) → float[source]

t_p_[x]+s by chain rule: prod(1_p_[x]+s+y) for y in range(t)

Parameters:

  • x – age of selection

  • s – years after selection

  • t – survives t years

q_x(x: int, s: int = 0, t: int = 1, u: int = 0) → float[source]

t|u_q_[x]+s = [x]+s survives u years, does not survive next t

Parameters:

  • x – age of selection

  • s – years after selection

  • u – survives u years, then

  • t – dies within next t years

e_x(x: int, s: int = 0, t: int = -999, curtate: int = True) → float[source]

Returns expected life time computed from select table

Parameters:

  • x – age of selection

  • s – years after selection

  • t – limit of expected future lifetime

frame(table: str = 'l') → DataFrame[source]

Returns select and ultimate table values as a DataFrame

Parameters:

table – table to return, one of [‘A’, ‘a’, ‘q’, ‘d’, ‘e’, ‘l’]

Examples

>>> table={21: [.00120, .00150, .00170, .00180],
>>>        22: [.00125, .00155, .00175, .00185],
>>>        23: [.00130, .00160, .00180, .00195]}
>>> life = SelectLife(verbose=True).set_table(q=table)
>>> print(life.frame('l').round(1))
>>> print(life.frame('q').round(6))