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Fractional-duration whole life reserves

fractional_duration_reserves.Rd

Computes fractional-duration whole life reserves using linear interpolation between the reserve immediately after the premium at duration \(t\) and the reserve at duration \(t+1\).

Usage

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

meanVx(x, t, i, tbl = NULL, model = NULL, ...)

Arguments

x

Issue age. May be scalar or vector.

t

Nonnegative integer duration. 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

tsVx() computes the reserve at fractional duration \(t+s\), where \(0 \le s \le 1\).

meanVx() computes the reserve at the midpoint of the policy year (\(s=0.5\)).

The fractional reserve is computed using

$$ {}_{t+s}V_x = ({}_tV_x + P_x)(1-s) + {}_{t+1}V_x s. $$

The function meanVx() is a convenience wrapper corresponding to \(s=0.5\).

Examples

tsVx(
  40,
  t = 10,
  s = 0.5,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.08762133

meanVx(
  40,
  t = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.08762133