Approximates the reserve at time `t` from a known reserve at time
`t + h`.
Usage
thiele_backward_step(V_next, P, delta, mu, benefit = 1, h = 1)
Arguments
- V_next
Reserve at time `t + h`.
- P
Premium rate.
- delta
Force of interest.
- mu
Nonnegative force of mortality at time `t`.
- benefit
Benefit amount.
- h
Positive step size.
Value
Numeric vector of reserve approximations.
Details
The implemented step is
$$
V_t =
\frac{
V_{t+h} - hP + h\mu B
}{
1 + h(\delta + \mu)
}.
$$
Examples
thiele_backward_step(
V_next = 1000,
P = 26.96,
delta = 0.058,
mu = 0.002,
benefit = 1000,
h = 1
)
#> [1] 919.8491