Gain or loss in a multiple-decrement model

Computes the gain or loss expression from Section 14.6.

Usage

gain_loss_md(
  Vt,
  G,
  r,
  e,
  i,
  b1,
  b2,
  s1 = 0,
  s2 = 0,
  q1,
  q2,
  Vt1,
  year_end_cause2 = FALSE,
  q1prime = NULL,
  q2prime = NULL
)

Arguments

Vt

Gross premium reserve at time \(t\).

G

Gross premium for the year.

r

Percent-of-premium expense factor.

e

Fixed expense at the beginning of the year.

i

Earned interest rate.

b1

Cause 1 benefit.

b2

Cause 2 benefit.

s1

Claim settlement expense for Cause 1.

s2

Claim settlement expense for Cause 2.

q1

Cause 1 decrement probability.

q2

Cause 2 decrement probability.

Vt1

Gross premium reserve at time \(t+1\).

year_end_cause2

Logical; if TRUE, use the year-end Cause 2 form.

q1prime

Single-decrement Cause 1 probability for the year-end Cause 2 case.

q2prime

Single-decrement Cause 2 probability for the year-end Cause 2 case.

Value

A numeric scalar.

Details

With within-year decrement probabilities, the function evaluates $$ [{}_{t}V^G + G(1-r) - e](1+i) - \left[(b^{(1)}+s^{(1)})q^{(1)} + (b^{(2)}+s^{(2)})q^{(2)} + p^{(\tau)} {}_{t+1}V^G \right] $$

If year_end_cause2 = TRUE, the Cause 2 decrement is treated as occurring only at year end, matching Equation (14.30).

Examples

gain_loss_md(
  Vt = 115.00, G = 16, r = 0, e = 3, i = 0.06,
  b1 = 1000, b2 = 110, s1 = 0, s2 = 0,
  q1 = 0.01, q2 = 0.10, Vt1 = 128.83
)
#> [1] 0.0213