Bayesian bivariate graduation and forecasting

Abstract

The estimation of survival functions is fundamental to the disciplines of reliability engineering, biostatistics, demography, and actuarial science. ln actuarial applications we deal with populations of insureds, annuitants, and pensioners. We need to estimate probabilities of individuals remaining in the populations and moving from the populations for reasons of death, change in health status, voluntary withdrawal, etc. Estimates of these probabilities aid actuaries in premium and reserve determination and, as a consequence, in developing investment strategies and cash flow projections.

Let there be K age groups in a life table. Suppose that for each age group a death rate has been observed for each of c ₁ calendar periods. We present a Bayesian approach to (1) estimation of the underlying death rates for the observation period (graduation), (2) estimation of the underlying death rates for C _a future calendar periods (extrapolation), and (3) prediction of the observed death rates for the c ₂ future calendar periods (forecasting).