actuarial

Define base class for actuarial math, with utility helpers and constants

MIT License. Copyright (c) 2022-2023 Terence Lim

class actuarialmath.actuarial.Actuarial

Bases: object

Define constants and common utility functions

Constants:

VARIANCE : select variance as the statistical moment to calculate

WHOLE : indicates that term of insurance or annuity is Whole Life

VARIANCE = -2

WHOLE = -999

static isclose(r: float, target: float = 0.0, abs_tol=1e-06) → bool

Is close to zero or target value

Parameters:

• r – value to test if close to zero or target

• target – target value, default is 0.0

static integral(fun: Callable[[float], float], lower: float, upper: float) → float

Compute integral of the function between lower and upper limits

Parameters:

• fun – function to integrate

• upper – upper limit

• lower – lower limit

static derivative(fun: Callable[[float], float], x: float) → float

Compute derivative of the function at a value

Parameters:

• fun – function to compute derivative

• x – value to compute derivative at

Examples

>>> print(Actuarial.derivative(fun=lambda x: x/50, x=25))

static solve(fun: Callable[[float], float], target: float, grid: float | Tuple | List, mad: bool = False) → float

Solve root, or parameter that minimizes absolute value, of a function

Parameters:

• fun – function to compute output given input values

• target – target value of function output

• grid – initial range of guesses

• root – whether to solve root (True), or minimize absolute function (False)

Returns:

value s.t. output of function fun(value) ~ target

Examples

>>> print(Actuarial.solve(fun=lambda omega: 1/omega,
>>>                       target=0.05, grid=[1, 100]))

add_term(t: int, n: int) → int

Add two terms, either term may be Whole Life

Parameters:

• t – first term to add

• n – second term to add

max_term(x: int, t: int, u: int = 0) → int

Decrease term t if adding deferral period u to (x) exceeds maxage

Parameters:

• x – age

• t – term of insurance or annuity, after deferral period

• u – term deferred

Returns:

value of term t adjusted by deferral and maxage s.t. maxage not exceeded