Backward Euler reserve path from maturity

Starting from a terminal reserve value at time T, computes reserves backward on a grid using the backward Euler-style Thiele step.

Usage

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

Arguments

times

Vector of times in increasing order.

V_terminal

Reserve at the final time.

P

Premium rate, scalar or vector of length length(times)-1.

delta

Force of interest, scalar or vector of length length(times)-1.

mu

Force of mortality, scalar or vector of length length(times)-1.

benefit

Benefit amount, scalar or vector of length length(times)-1.

Value

Numeric vector of reserve values on the grid.

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