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Profit vector for a discrete profit-analysis model

Pr_vector_disc.Rd

Computes expected profit by policy year for a discrete contract with up to two decrements. The first element is the negative pre-contract expense.

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

Numeric vector of gross premium reserves with length n + 1, including the issue-time and terminal reserves.

G

Gross premium by policy year.

i

Annual effective interest rate by policy year. Values must be greater than -1.

r

Percent-of-premium expense rate by policy year. Values must lie in [0, 1].

e

Fixed expense by policy year.

q1

Probability of the first decrement by policy year.

q2

Probability of the second decrement by policy year.

b1

Benefit payable on the first decrement.

b2

Benefit payable on the second decrement.

s1

Settlement expense associated with the first decrement.

s2

Settlement expense associated with the second decrement.

p_tau

Optional in-force probability by policy year. If omitted, it is calculated as 1 - q1 - q2.

pre_contract_expense

Nonnegative scalar pre-contract expense.

Value

A named numeric vector of length n + 1.

Details

For policy year \(k\), the expected profit is $$ [V_{k-1} + G_k(1-r_k)-e_k](1+i_k) - [(b_k^{(1)}+s_k^{(1)})q_k^{(1)} +(b_k^{(2)}+s_k^{(2)})q_k^{(2)} +V_kp_k^{(\tau)}]. $$

Scalar yearly inputs are recycled to the number of policy years determined by length(V) - 1.

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