Projected asset share path \({}_{k}AS\)

Computes projected asset shares recursively using Equations (14.5b) and (14.6b) of Chapter 14, with optional support for a survival benefit payable at the end of year \(k\).

Usage

AS_path(AS0, G, r, e, b1, b2, q1, q2, p_tau, i, b3 = NULL)

Arguments

AS0

Initial asset share \({}_{0}AS\).

G

Level annual premium.

r

Numeric vector of percent-of-premium expense factors.

e

Numeric vector of fixed contract expenses.

b1

Numeric vector of Cause 1 benefit amounts.

b2

Numeric vector of Cause 2 benefit amounts.

q1

Numeric vector of Cause 1 decrement probabilities.

q2

Numeric vector of Cause 2 decrement probabilities.

p_tau

Numeric vector of in-force probabilities.

i

Effective annual interest rate.

b3

Optional numeric vector of survival benefit amounts payable at the end of year \(k\) conditional on survival through year \(k\). Defaults to a zero vector.

Value

A data frame with columns k and AS.

Details

For policy year \(k\), $$ [{}_{k-1}AS + G(1-r_k) - e_k](1+i) = b_k^{(1)} q_{x+k-1}^{(1)} + b_k^{(2)} q_{x+k-1}^{(2)} + p_{x+k-1}^{(\tau)} \left(b_k^{(3)} + {}_{k}AS\right) $$ so that $$ {}_{k}AS = \frac{[{}_{k-1}AS + G(1-r_k) - e_k](1+i) - b_k^{(1)} q_{x+k-1}^{(1)} - b_k^{(2)} q_{x+k-1}^{(2)}}{p_{x+k-1}^{(\tau)}} - b_k^{(3)} $$