% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/reserve_ch10_ext.R
\name{thiele_backward_step}
\alias{thiele_backward_step}
\title{One backward numerical step for Thiele's equation}
\usage{
thiele_backward_step(V_next, P, delta, mu, benefit = 1, h = 1)
}
\arguments{
\item{V_next}{Reserve at time `t + h`.}

\item{P}{Premium rate.}

\item{delta}{Force of interest.}

\item{mu}{Nonnegative force of mortality at time `t`.}

\item{benefit}{Benefit amount.}

\item{h}{Positive step size.}
}
\value{
Numeric vector of reserve approximations.
}
\description{
Approximates the reserve at time `t` from a known reserve at time
`t + h`.
}
\details{
The implemented step is
\deqn{
V_t =
\frac{
V_{t+h} - hP + h\mu B
}{
1 + h(\delta + \mu)
}.
}
}
\examples{
thiele_backward_step(
  V_next = 1000,
  P = 26.96,
  delta = 0.058,
  mu = 0.002,
  benefit = 1000,
  h = 1
)
}
