Love and death: A Freund model with frailty

Abstract

a b s t r a c tWe introduce new models for analyzing the mortality dependence between individuals in a couple. The mortality risk dependence is usually taken into account in the actuarial literature by introducing special copulas with continuous density. This practice implies symmetric effects on the remaining lifetime of the surviving spouse. The new model allows for both asymmetric reactions by means of a Freund model, and risk dependence by means of an unobservable common risk factor (or frailty). These models allow for distinguishing in the lifetime dependence the component due to common lifetime (frailty) from the jump in mortality intensity upon death of spouse (Freund model). The model is applied to the pricing of insurance products such as joint life policy, last survivor insurance, or contracts with reversionary annuities. A discussion of identification is also provided.

Longevity risk and capital markets: the 2018–19 update

“…Darkiewicz & Hoedemakers, 2004;Li & Lee, 2005;Cairns et al, 2011b;Dowd et al, 2011b;Jarner & Kryger, 2011;Njenga & Sherris, 2011;Börger & Ruß, 2012;Torri & Vaupel, 2012;D'Amato et al, 2014;Raftery et al, 2014;Zhou et al, 2014;Chen et al, 2015;Kleinow, 2015;Biffis et al, 2017;Li et al, 2015cDe Jong et al, 2016;Enchev et al, 2017;Zhu et al, 2017;Hunt & Blake, 2018;Pascariu et al, 2018;Wang et al, 2018;Yang et al, 2020;Chang et al, 2020) • Cause-of-death mortality modelling (e.g. Beard, 1971;McNown & Rogers, 1992;Christensen & Vaupel, 1996;Hanewald, 2011;Murphy & Di Cesare, 2012;Arnold & Sherris, 2015;Gourieroux & Lu, 2015;Alai et al, 2018;Boumezoued et al, 2018;Yue et al, 2018;Li et al, 2019;Lyu et al, 2020) • Longevity risk and financial innovation (improvements in the analysis and design of longevity-linked products) (e.g. Gong & Webb, 2010;Stevens at al., 2010;Richter & Weber, 2011;Cocco & Gomes, 2012;…”

Still Living With Mortality: The Longevity Risk Transfer Market After One Decade

“…Academic researchers have recently begun experimenting with the introduction of causal variables in their mortality models (e.g. Hanewald, 2011;Gaille & Sherris, 2011;Alai et al, 2014a;Gourieroux & Lu, 2015;Cairns et al, 2017a). Practitioners also started to use post code as a measure of socio-economic class (SEC) in their proprietary mortality models, especially for pricing annuities.…”

Long Term Care and Longevity

“…To our best knowledge, the idea of introducing explicitly a regime change dates back to Freund (1961), who considered only the case of constant hazards; it is later generalized to the previous general form by Tosch and Holmes (1980). Recently this latent model has been generalized to include static frailty [see Abbring and Van den Berg (2003b)] and an extended version applied to the pricing of joint insurance contracts for couples [see Gouriéroux and Lu (2013)]. The aim of our paper is to introduce dynamic (common) frailty featuring trends and able to capture the stochastic longevity phenomenon.…”