% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/reserve_ch11.R
\name{full_preliminary_term}
\alias{full_preliminary_term}
\alias{alphaF}
\alias{betaF}
\alias{tVFx}
\title{Full preliminary term modified premiums and reserves}
\usage{
alphaF(x, i, tbl = NULL, model = NULL, ...)

betaF(x, i, tbl = NULL, model = NULL, ...)

tVFx(x, t, i, tbl = NULL, model = NULL, ...)
}
\arguments{
\item{x}{Issue age. May be scalar or vector.}

\item{i}{Effective annual interest rate. May be scalar or vector.}

\item{tbl}{Optional life table object.}

\item{model}{Optional parametric survival model.}

\item{...}{Additional parameters passed to the actuarial functions.}

\item{t}{Nonnegative integer duration. May be scalar or vector.}
}
\value{
A numeric vector of modified premiums or reserves.
}
\description{
Computes modified premiums and reserves under the full preliminary term
method for whole-life insurance.
}
\details{
\code{alphaF()} computes the first-year modified premium
\eqn{\alpha^F = vq_x}.

\code{betaF()} computes the renewal modified premium
\eqn{\beta^F = P_{x+1}}.

\code{tVFx()} computes the full preliminary term reserve. The reserve is
zero at durations 0 and 1. For \eqn{t > 1}, it equals the net level premium
reserve at duration \eqn{t - 1} for a policy issued at age \eqn{x + 1}.


Under the full preliminary term method, the first policy year is treated
as one-year term insurance. The first-year modified premium is therefore
the actuarial present value of one-year term insurance at age \eqn{x}.

Renewal premiums are based on a whole-life policy issued one year later,
at age \eqn{x + 1}. Accordingly, reserves after the first policy year are
obtained from the corresponding net level premium reserve for that
deferred issue age.
}
\examples{
alphaF(
  x = 40,
  i = 0.05,
  model = "uniform",
  omega = 100
)

betaF(
  x = 40,
  i = 0.05,
  model = "uniform",
  omega = 100
)

tVFx(
  x = 40,
  t = 5,
  i = 0.05,
  model = "uniform",
  omega = 100
)

}
