Application of Frailty-Based Mortality Models Using Generalized Linear Models

Abstract

Two families of frailty models – Makeham/Gompertz-gamma and Gompertz-inverse Gaussian – have been considered to graduate insurance-based mortality data. The aims of this exercise are twofold. The first aim is to make use of generalized linear models and to evaluate these against traditional techniques. The second aim is to measure the scale of individual heterogeneity in insurance-based populations. The results indicate that (subject to issues of identifiability) there is evidence of frailty in these populations.

Adverse Selection in the Annuity Market and the Role for Social Security

“…An alternative approach taken by Butt and Haberman (2004) and Einav et al (2010) is to make a parametric assumption on H t as well as the initial distribution of θ and estimate these parameters using only the life table data. The parametric assumption puts restriction on the variance of θ.…”

Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz’ law of mortality

“…The heterogeneous mortality intensity of Gompertz distribution with Gamma distributed frailty is also related to a simplified version of Perks' well known mortality intensity from 1932 (see for example Butt and Haberman (2004)). The heterogeneous mortality intensity is…”

“…Butt and Haberman (2004). Wang and Brown (1998) have fitted the Gompertz distribution with Gamma distributed frailty to the 1994 Group Annuity Reserving Table of The formulas above allow us to identify the baseline population density and the frailty density independently resulting in the following heterogeneous density for X + Z :…”

“…Continuous heterogeneous mortality models with multiplicative frailty were originally developed by Vaupel et al (1979). A recent actuarial application of frailty-based mortality models is presented by Butt and Haberman (2004). A general disadvantage of the present form of these models is that they cannot be adequately tested because frailty cannot be identified directly from the data.…”

Survival models in a dynamic context: a survey

“…However, very recent contributions show interest for this topic within the actuarial community. See Butt and Haberman (2002), Wang and Brown (1998), the latter being devoted to mortality forecasts.…”