Mortality improvement projection functions — mortality_improvement

Functions for projecting one-year death and survival probabilities under mortality improvement and evaluating annuity values under projected mortality.

Usage

qx_proj(qx_base, AAx, base_year, proj_year)

px_proj(qx_base, AAx, base_year, proj_year)

tpx_improved(x0, n, qx_base_vec, AAx_vec, base_year, issue_year)

axn_improved(x0, n, i, qx_base_vec, AAx_vec, base_year, issue_year)

naxn_improved(x0, u, n, i, qx_base_vec, AAx_vec, base_year, issue_year)

ax_improved(x0, i, qx_base_vec, AAx_vec, base_year, issue_year)

Arguments

qx_base: Base-year one-year death probability.
AAx: Mortality improvement factor.
base_year: Base year.
proj_year: Projection year. May be scalar or vector.
x0: Issue age.
n: Number of years.
qx_base_vec: Base-year death probabilities for successive ages.
AAx_vec: Mortality improvement factors for successive ages.
issue_year: Issue year.
i: Effective annual interest rate.
u: Deferral period in years.

Value

Numeric vector of projected one-year death probabilities.

Details

The standard projection used is $$q_x^{[Y]} = q_x^{[B]} (1 - AA_x)^{Y-B},$$ where $B$ is the base year, $Y$ is the projection year, and $AA_x$ is the mortality improvement factor at age $x$.