Profit vector for a discrete profit-analysis model

Computes the Chapter 17 profit vector $$ \mathbf{Pr} = (Pr_0, Pr_1, \dots, Pr_n) $$ where \(Pr_0\) is the negative pre-contract expense and the yearly expected profit values are calculated from the general discrete expression in Equation (17.1).

Usage

Pr_vector_disc(
  V,
  G,
  i,
  r = 0,
  e = 0,
  q1,
  q2 = 0,
  b1,
  b2 = 0,
  s1 = 0,
  s2 = 0,
  p_tau = NULL,
  pre_contract_expense = 0
)

Arguments

V

Vector of gross premium reserves \({}_tV^G\) of length \(n+1\), including the issue-time reserve and the terminal reserve.

G

Gross premium vector for policy years 1 through \(n\).

i

Interest-rate vector for policy years 1 through \(n\).

r

Percent-of-premium expense vector.

e

Fixed expense vector.

q1

First decrement probabilities, typically death.

q2

Second decrement probabilities, typically surrender or lapse. Defaults to 0.

b1

Benefit vector for decrement 1.

b2

Benefit vector for decrement 2. Defaults to 0.

s1

Settlement-expense vector for decrement 1. Defaults to 0.

s2

Settlement-expense vector for decrement 2. Defaults to 0.

p_tau

Optional vector of in-force probabilities \(p_{x+t}^{(\tau)}\). If omitted, it is computed as \(1-q^{(1)}-q^{(2)}\).

pre_contract_expense

Positive pre-contract expense amount. The returned first element is \(Pr_0 = -\text{pre\_contract\_expense}\).

Value

Numeric vector of length \(n+1\).

Details

This implementation allows for two decrements, typically death and withdrawal/surrender.

Examples

V <- c(0, 5.66, 6.17, 0)
qx <- c(0.00142, 0.00153, 0.00166)
Pr_vector_disc(
  V = V, G = 95, i = 0.06, r = 0.05, e = 10,
  q1 = qx, b1 = 50000, pre_contract_expense = 15
)
#>        Pr0        Pr1        Pr2        Pr3 
#> -15.000000   8.413037   8.404040   8.605200