% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/reserve_ch10_ext.R
\name{thiele_backward_path}
\alias{thiele_backward_path}
\title{Backward Euler reserve path from maturity}
\usage{
thiele_backward_path(times, V_terminal, P, delta, mu, benefit = 1)
}
\arguments{
\item{times}{Vector of times in increasing order.}

\item{V_terminal}{Reserve at the final time.}

\item{P}{Premium rate, scalar or vector of length length(times)-1.}

\item{delta}{Force of interest, scalar or vector of length length(times)-1.}

\item{mu}{Force of mortality, scalar or vector of length length(times)-1.}

\item{benefit}{Benefit amount, scalar or vector of length length(times)-1.}
}
\value{
Numeric vector of reserve values on the grid.
}
\description{
Starting from a terminal reserve value at time T, computes reserves
backward on a grid using the backward Euler-style Thiele step.
}
\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)
}
