Love and death: A Freund model with frailty

Christian Gouriéroux and Yang Lu
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Christian Gouriéroux: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We 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.

Keywords: Frailty; Freund model; Copula; Life Insurance; Coupled Lives; Broken-Heart; Last Survivor Insurance; Competing Risks (search for similar items in EconPapers)
Date: 2015
Note: View the original document on HAL open archive server: https://hal.science/hal-02419013v1
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Citations: View citations in EconPapers (11)

Published in Insurance: Mathematics and Economics, 2015, 63, pp.191-203. ⟨10.1016/j.insmatheco.2015.03.016⟩

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Related works:
Journal Article: Love and death: A Freund model with frailty (2015)
Working Paper: Love and Death: A Freund Model with Frailty (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02419013

DOI: 10.1016/j.insmatheco.2015.03.016

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