Whole life gross premium and expense reserves — gross_premium_expense

Computes prospective gross premium and expense reserves for fully discrete whole life insurance after issue.

Usage

tVGx(
  x,
  t,
  i,
  G,
  benefit = 1,
  renewal_premium_pct = 0,
  renewal_policy_exp = 0,
  settlement_exp = 0,
  tbl = NULL,
  model = NULL,
  ...
)

tVEx(
  x,
  t,
  i,
  G,
  benefit = 1,
  renewal_premium_pct = 0,
  renewal_policy_exp = 0,
  settlement_exp = 0,
  tbl = NULL,
  model = NULL,
  ...
)

Arguments

x: Issue age. May be scalar or vector.
t: Nonnegative integer duration. May be scalar or vector.
i: Effective annual interest rate. May be scalar or vector.
G: Gross annual premium. May be scalar or vector.
benefit: Insurance benefit amount.
renewal_premium_pct: Renewal percent-of-premium expense in $[0,1]$.
renewal_policy_exp: Renewal per-policy expense.
settlement_exp: Settlement expense paid at death.
tbl: Optional life table object.
model: Optional parametric survival model.
...: Additional parameters passed to the actuarial functions.

Value

A numeric vector of reserve values.

Details

tVGx() computes the prospective gross premium reserve.

tVEx() computes the corresponding expense reserve, defined as the difference between the gross premium reserve and the net benefit reserve.

The gross premium reserve is calculated as

$$ {}_tV_x^G = (b+s)A_{x+t} - \left[(1-r)G-e\right]\ddot{a}_{x+t}, $$

where

$b$ is the insurance benefit,
$s$ is the settlement expense,
$G$ is the gross annual premium,
$r$ is the renewal percent-of-premium expense, and
$e$ is the renewal per-policy expense.

The expense reserve is obtained as the gross premium reserve minus the corresponding net benefit reserve.

Examples

tVGx(
  x = 40,
  t = 10,
  i = 0.05,
  G = 0.03,
  benefit = 1,
  renewal_premium_pct = 0.10,
  renewal_policy_exp = 0.002,
  settlement_exp = 0.02,
  model = "uniform",
  omega = 100
)
#> [1] 0.0391081

tVEx(
  x = 40,
  t = 10,
  i = 0.05,
  G = 0.03,
  benefit = 1,
  renewal_premium_pct = 0.10,
  renewal_policy_exp = 0.002,
  settlement_exp = 0.02,
  model = "uniform",
  omega = 100
)
#> [1] -0.03339664