Continuous premium approximation \(\overline{P}\) by trapezoidal rule

Approximates the annual continuous premium in the disability model allowing for recovery, as in Example 14.18.

Usage

Pbar_trapz_ms(t, tp00, tp01, delta, mu02, mu12, B02 = 1, B12 = 1, R = 0)

Arguments

t

Numeric vector of time points.

tp00

Numeric vector of values \({}_{t}p_{x}^{00}\).

tp01

Numeric vector of values \({}_{t}p_{x}^{01}\).

delta

Force of interest.

mu02

Function of time returning \(\mu_{x+t}^{02}\).

mu12

Function of time returning \(\mu_{x+t}^{12}\).

B02

Benefit payable on death while healthy.

B12

Benefit payable on death while disabled.

R

Continuous income rate while disabled.

Value

A numeric scalar.

Details

The numerator is $$ \int v^t \left[{}_{t}p_{x}^{00}\mu_{x+t}^{02}B^{02} + {}_{t}p_{x}^{01}\mu_{x+t}^{12}B^{12} + {}_{t}p_{x}^{01}R \right] dt $$ and the denominator is $$ \int v^t {}_{t}p_{x}^{00} dt $$

Examples

mu01 <- function(t) 0.10 * t + 0.20
mu02 <- function(t) 0.20
mu10 <- function(t) 0.50
mu12 <- function(t) 0.125 * t + 0.20

ex1410 <- tp00_tp01_euler(
  h = 0.10, n = 2.0,
  mu01 = mu01, mu02 = mu02, mu10 = mu10, mu12 = mu12
)

Pbar_trapz_ms(
  t = ex1410$t,
  tp00 = ex1410$tp00,
  tp01 = ex1410$tp01,
  delta = 0.04,
  mu02 = mu02,
  mu12 = mu12,
  B02 = 1000,
  B12 = 1000,
  R = 1000
)
#> [1] 446.9451