% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/chapter17_profit_analysis.R
\name{V_zeroized}
\alias{V_zeroized}
\title{Zeroized reserves for a discrete death-only contract}
\usage{
V_zeroized(qx, i, G, benefit, r = 0, e = 0, V_terminal = 0, floor_zero = TRUE)
}
\arguments{
\item{qx}{Mortality vector.}

\item{i}{Interest-rate vector.}

\item{G}{Gross premium vector.}

\item{benefit}{Death-benefit vector.}

\item{r}{Percent-of-premium expense vector.}

\item{e}{Fixed-expense vector.}

\item{V_terminal}{Terminal reserve. Defaults to 0.}

\item{floor_zero}{Logical; if \code{TRUE}, negative reserves are reset to 0.}
}
\value{
Numeric vector of zeroized reserves of length \eqn{n+1}.
}
\description{
Computes the zeroized reserve sequence by backward recursion, setting
negative reserves equal to zero.
}
\details{
For a death-only contract with no settlement expense and no second
decrement, the recursion sets
\deqn{
Pr_{t+1} = ({}_tV^Z + G_{t+1}(1-r_{t+1}) - e_{t+1})(1+i_{t+1})
- [Bq_{x+t} + {}_{t+1}V^Z p_{x+t}]
}
equal to zero, solving backward for \eqn{{}_tV^Z}.
}
\examples{
V_zeroized(
  qx = c(.015, .017, .019, .021, .024),
  i = 0.06,
  G = 19279,
  benefit = 1000000,
  e = 240
)

}
