% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/premium_ch9.R
\name{premium_functions}
\alias{premium_functions}
\alias{Px}
\alias{Pxn1}
\alias{PnEx}
\alias{Pxn}
\alias{tPx}
\alias{tPxn1}
\alias{tPnEx}
\alias{tPxn}
\alias{PnAx}
\alias{tPnAx}
\alias{Pbarx}
\alias{Pbarxn1}
\alias{Pbarxn}
\alias{PbarAbarx}
\alias{PbarAbarxn1}
\alias{PbarAbarxn}
\alias{Px_m}
\alias{Pxn1_m}
\alias{Pxn_m}
\alias{PnAx_m}
\alias{EL0x}
\alias{varL0x}
\alias{EL0xn1}
\alias{varL0xn1}
\alias{EL0xn}
\alias{varL0xn}
\alias{EL0barAbarx}
\alias{varL0barAbarx}
\alias{Gx}
\title{Premium, loss, and expense functions}
\usage{
Px(x, i, tbl = NULL, model = NULL, ...)

Pxn1(x, n, i, tbl = NULL, model = NULL, ...)

PnEx(x, n, i, tbl = NULL, model = NULL, ...)

Pxn(x, n, i, tbl = NULL, model = NULL, ...)

tPx(x, t, i, tbl = NULL, model = NULL, ...)

tPxn1(x, n, t, i, tbl = NULL, model = NULL, ...)

tPnEx(x, n, t, i, tbl = NULL, model = NULL, ...)

tPxn(x, n, t, i, tbl = NULL, model = NULL, ...)

PnAx(x, n, i, tbl = NULL, model = NULL, ...)

tPnAx(x, n, t, i, tbl = NULL, model = NULL, ...)

Pbarx(x, i, model, ..., tol = 1e-10)

Pbarxn1(x, n, i, model, ...)

Pbarxn(x, n, i, model, ...)

PbarAbarx(x, i, model, ..., tol = 1e-10)

PbarAbarxn1(x, n, i, model, ...)

PbarAbarxn(x, n, i, model, ...)

Px_m(x, m, i, tbl = NULL, model = NULL, ...)

Pxn1_m(x, n, m, i, tbl = NULL, model = NULL, ...)

Pxn_m(x, n, m, i, tbl = NULL, model = NULL, ...)

PnAx_m(x, n, m, i, tbl = NULL, model = NULL, ...)

EL0x(x, P, i, tbl = NULL, model = NULL, ...)

varL0x(x, P, i, tbl = NULL, model = NULL, ..., tol = 1e-12, k_max = 5000)

EL0xn1(x, n, P, i, tbl = NULL, model = NULL, ...)

varL0xn1(x, n, P, i, tbl = NULL, model = NULL, ...)

EL0xn(x, n, P, i, tbl = NULL, model = NULL, ...)

varL0xn(x, n, P, i, tbl = NULL, model = NULL, ...)

EL0barAbarx(x, P, i, model, ..., tol = 1e-10)

varL0barAbarx(x, P, i, model, ...)

Gx(
  x,
  i,
  benefit = 1,
  first_premium_pct = 0,
  renewal_premium_pct = 0,
  first_policy_exp = 0,
  renewal_policy_exp = 0,
  settlement_exp = 0,
  tbl = NULL,
  model = NULL,
  ...
)
}
\arguments{
\item{x}{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 name.}

\item{...}{Additional arguments passed to survival-model functions.}

\item{n}{Term. May be scalar or vector of nonnegative integers.}

\item{t}{Premium-paying period. May be scalar or vector of nonnegative integers.}

\item{tol}{Numerical tolerance for functions that truncate infinite sums.}

\item{m}{Number of payments per year. Must be a positive integer scalar.}

\item{P}{Premium amount or premium rate. May be scalar or vector.}

\item{k_max}{Maximum summation horizon for functions that truncate infinite sums.}

\item{benefit}{Benefit amount. May be scalar or vector.}

\item{first_premium_pct}{First-year premium expense proportion. May be scalar or vector.}

\item{renewal_premium_pct}{Renewal premium expense proportion. May be scalar or vector.}

\item{first_policy_exp}{First-year fixed expense. May be scalar or vector.}

\item{renewal_policy_exp}{Renewal fixed expense after the first year. May be scalar or vector.}

\item{settlement_exp}{Settlement expense incurred at benefit payment. May be scalar or vector.}
}
\value{
Numeric vector.
}
\description{
Functions for net and gross premiums, present-value-of-loss moments,
continuous-payment premium rates, and premiums payable more frequently
than annually.
}
\details{
The functions include:
\itemize{
  \item net annual premiums under the equivalence principle,
  \item limited-payment premiums,
  \item continuous-payment premium rates,
  \item fully continuous premium rates,
  \item true fractional premiums,
  \item present-value-of-loss means and variances,
  \item a basic gross premium formula for whole life insurance.
}

The discrete premium functions may be evaluated from either a life table
supplied through \code{tbl} or a parametric survival model supplied through
\code{model}. Continuous-payment premium functions are evaluated through
the corresponding continuous insurance and annuity functions.

Scalar inputs retain their existing behavior. Where mathematically
meaningful, numeric inputs may also be vectors. Inputs are evaluated
elementwise when they have a common length, and scalar inputs are recycled.
}
