policyvalues

Policy Values - Computes present value of future losses and reserves

MIT License. Copyright 2022-2023 Terence Lim

class actuarialmath.policyvalues.PolicyValues(**kwargs)[source]

Bases: Premiums

Compute net and gross future losses and policy values

net_future_loss(A: float, A1: float, b: int = 1) → float[source]

Shortcut for net policy value with WL or Endowment Insurance factors

Parameters:

  • A – insurance factor at age (x)

  • A1 – insurance factor at t years after x

  • b – benefit amount

net_variance_loss(A1: float, A2: float, A: float = 0, b: int = 1) → float[source]

Variance of net loss with WL or Endowment Insurance factors

Parameters:

  • A – insurance factor at age (x)

  • A1 – first moment of insurance factor at t years after x

  • A2 – insurance factor at double force of interest t years after x

  • b – benefit amount

net_policy_variance(x, s: int = 0, t: int = 0, b: int = 1, n: int = -999, endowment: int = 0, discrete: bool = True) → float[source]

Variance of net future loss for WL or Endowment Insurance only

Parameters:

  • x – age of selection

  • s – years after selection

  • n – term of life insurance

  • t – years after issue to compute policy variance

  • b – benefit amount

  • endowment – endowment amount

  • discrete – annuity due (True) or continuous (False)

net_policy_value(x: int, s: int = 0, t: int = 0, b: int = 1, n: int = -999, endowment: int = 0, discrete: bool = True) → float[source]

Net policy value assuming net premiums from equivalence principle: E[L_t]

Parameters:

  • x – age initially insured

  • s – years after selection

  • n – term of life insurance

  • t – years after issue to compute policy variance

  • b – benefit amount

  • endowment – endowment amount

  • discrete – discrete/annuity due (True) or continuous (False)

gross_future_loss(A: float | None = None, a: float | None = None, contract: Contract | None = None) → float[source]

Shortcut for gross policy value with WL or Endowment Insurance factors

Parameters:

  • A – insurance factor at age (x)

  • a – annuity factor at age (x)

  • contract – policy contract terms and expenses

gross_variance_loss(A1: float, A2: float = 0, contract: Contract | None = None) → float[source]

Variance of gross loss with WL or endowment insurance factors

Parameters:

  • A1 – insurance factor

  • A2 – insurance factor at double the force of interest

  • policy – policy terms and expenses

gross_policy_variance(x: int, s: int = 0, t: int = 0, n: int = -999, contract: Contract | None = None) → float[source]

Variance of gross policy value for WL and Endowment Insurance only

Parameters:

  • x – age initially insured

  • s – years after selection

  • n – term of life insurance

  • t – years after issue to compute policy variance

  • contract – policy contract terms and expenses

gross_policy_value(x: int, s: int = 0, t: int = 0, n: int = -999, contract: Contract | None = None) → float[source]

Gross policy values for insurance: t_V = E[L_t]

Parameters:

  • x – age initially insured

  • s – years after selection

  • t – number of years of premiums paid

  • n – term of insurance

  • contract – policy contract terms

L_from_t(t: float, contract: Contract | None = None) → float[source]

PV of Loss L(t) at time of death t = T_x

Parameters:

  • t – year of death

  • contract – policy contract

L_from_prob(x: int, prob: float, contract: Contract | None = None) → float[source]

Percentile of PV future loss r.v. L given probability

Parameters:

  • x – age

  • prob – probability threshold

  • contract – policy contract

L_to_t(L: float, contract: Contract | None = None) → float[source]

Time of death T_x s.t. PV future loss is no more than L

Parameters:

  • L – PV of future loss

  • contract – policy contract terms and expenses

L_to_prob(x: int, L: float, contract: ~actuarialmath.policyvalues.Contract = <actuarialmath.policyvalues.Contract object>) → float[source]

Probability such that PV of future loss r.v. is no more than L”

Parameters:

  • x – age selected

  • L – PV of future loss

  • contract – policy contract terms and expenses

L_plot(x: int, s: int = 0, stop: int = 0, T: float | None = None, contract: Contract | None = None, ax: Any = None, dual: bool = False, title: str | None = None, color: str = 'r', alpha: float = 0.3) → float | None[source]

Plot PV of future loss r.v. L vs time of death T_x

Parameters:

  • x – age selected

  • s – years after selection

  • stop – time to end plot

  • contract – policy contract terms and expenses

  • T – point in time to indicate probability and loss values

  • ax – figure object to plot in

  • title – title of plot

  • dual – whether to plot survival function on secondary axis

  • color – color to plot curve

  • alpha – transparency of plot area

class actuarialmath.policyvalues.Contract(premium: float = 1, initial_policy: float = 0, initial_premium: float = 0, renewal_policy: float = 0, renewal_premium: float = 0, settlement_policy: float = 0, benefit: float = 1, endowment: float = 0, T: int = -999, discrete: bool = True)[source]

Bases: Actuarial

Set and retrieve policy contract terms

Parameters:

  • premium – level premium amount

  • benefit – insurance death benefit amount

  • settlement_policy – settlement expense per policy

  • endowment – endowment benefit amount

  • initial_policy – first year total expense per policy

  • initial_premium – first year total premium per $ of gross premium

  • renewal_policy – renewal expense per policy

  • renewal_premium – renewal premium per $ of gross premium

  • discrete – annuity due (True) or continuous (False)

  • T – term of insurance

  • discrete – annuity due (True) or continuous (False)

set_contract(**terms) → Any[source]

Update any existing policy contract terms

Parameters:

**kwargs – one or more contract policy terms, and its value to update

property premium_terms: Dict

Dict of terms required for calculating gross premiums

Examples

>>> life = PolicyValues().set_interest(i=0.04)
>>> contract = Contract(premium=2.338, benefit=100, initial_premium=.1,
>>>                     renewal_premium=0.05)
>>> contract.premium = life.gross_premium(a=12, A=life.insurance_twin(a),
>>>                                       **contract.premium_terms)
renewals(t: int = 0) → Contract[source]

Returns contract object with initial terms set to renewal terms

Parameters:

t – number of years after initial

property renewal_profit: float

Renewal dollar profit (premium less renewal expenses)

property initial_cost: float

Total initial cost (net of renewal component of expenses and premiums)

property claims_cost: float

Total claims cost (death benefit + settlement expense)