Zeroized reserves for a discrete death-only contract

Computes the zeroized reserve sequence by backward recursion, setting negative reserves equal to zero.

Usage

V_zeroized(qx, i, G, benefit, r = 0, e = 0, V_terminal = 0, floor_zero = TRUE)

Arguments

qx

Mortality vector.

i

Interest-rate vector.

G

Gross premium vector.

benefit

Death-benefit vector.

r

Percent-of-premium expense vector.

e

Fixed-expense vector.

V_terminal

Terminal reserve. Defaults to 0.

floor_zero

Logical; if TRUE, negative reserves are reset to 0.

Value

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

Details

For a death-only contract with no settlement expense and no second decrement, the recursion sets $$ Pr_{t+1} = ({}_tV^Z + G_{t+1}(1-r_{t+1}) - e_{t+1})(1+i_{t+1}) - [Bq_{x+t} + {}_{t+1}V^Z p_{x+t}] $$ equal to zero, solving backward for \({}_tV^Z\).

Examples

V_zeroized(
  qx = c(.015, .017, .019, .021, .024),
  i = 0.06,
  G = 19279,
  benefit = 1000000,
  e = 240
)
#>       V0       V1       V2       V3       V4       V5 
#>    0.000    0.000 2679.540 4099.544 3602.509    0.000