Full preliminary term modified premiums and reserves

Computes modified premiums and reserves under the full preliminary term method for whole-life insurance.

Usage

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

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

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

Arguments

x

Issue age. May be scalar or vector.

i

Effective annual interest rate. May be scalar or vector.

tbl

Optional life table object.

model

Optional parametric survival model.

...

Additional parameters passed to the actuarial functions.

t

Nonnegative integer duration. May be scalar or vector.

Value

A numeric vector of modified premiums or reserves.

Details

alphaF() computes the first-year modified premium \(\alpha^F = vq_x\).

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

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

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 \(x\).

Renewal premiums are based on a whole-life policy issued one year later, at age \(x + 1\). 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
)
#> [1] 0.01587302

betaF(
  x = 40,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.02240155

tVFx(
  x = 40,
  t = 5,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.02773584