Fractional-duration term and endowment reserves

Computes fractional-duration reserves for term and endowment insurance using linear interpolation between the reserve immediately after the premium at duration \(t\) and the reserve at duration \(t+1\).

Usage

tsVxn(x, n, t, s, i, tbl = NULL, model = NULL, ...)

tsVxn1(x, n, t, s, i, tbl = NULL, model = NULL, ...)

Arguments

x

Issue age. May be scalar or vector.

n

Positive integer term. May be scalar or vector.

t

Nonnegative integer duration satisfying \(t < n\). May be scalar or vector.

s

Fractional duration in \([0,1]\). May be scalar or vector.

i

Effective annual interest rate. May be scalar or vector.

tbl

Optional life table object.

model

Optional parametric survival model.

...

Additional parameters passed to the actuarial functions.

Value

A numeric vector of reserve values.

Details

tsVxn() computes the fractional-duration reserve for endowment insurance.

tsVxn1() computes the fractional-duration reserve for term insurance.

The fractional reserve is computed using

$$ {}_{t+s}V = ({}_tV + P)(1-s) + {}_{t+1}V s. $$

The premium \(P\) is the net annual premium for the corresponding insurance contract (term or endowment).

Examples

tsVxn(
  40,
  n = 20,
  t = 10,
  s = 0.5,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.388849

tsVxn1(
  40,
  n = 20,
  t = 10,
  s = 0.5,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.02775327