Backward reserve path from a terminal value

Starting from a terminal reserve at the final time, computes reserves backward over a strictly increasing time grid using `thiele_backward_step()`.

Usage

thiele_backward_path(times, V_terminal, P, delta, mu, benefit = 1)

Arguments

times

Finite numeric vector of strictly increasing times.

V_terminal

Finite scalar reserve at the final time.

P

Premium rate, scalar or vector with one value per time step.

delta

Force of interest, scalar or vector with one value per step.

mu

Nonnegative force of mortality, scalar or vector with one value per step.

benefit

Benefit amount, scalar or vector with one value per step.

Value

Numeric vector of reserve values corresponding to `times`.

Examples

times <- seq(19, 20, by = 0.25)

thiele_backward_path(
  times,
  V_terminal = 1000,
  P = 26.96,
  delta = 0.058,
  mu = 0.002,
  benefit = 1000
)
#> [1]  918.1329  938.1449  958.4570  979.0739 1000.0000