A General Semi-Markov Model for Coupled Lifetimes

Min Ji and Rui Zhou

North American Actuarial Journal, 2019, vol. 23, issue 1, 98-119

Abstract: Joint-life annuities with a high last survivor benefit play an important role in the optimal annuity portfolio for a retired couple. The dependence between coupled lifetimes is crucial for valuing joint-life annuities. Existing bivariate modeling of coupled lifetimes is based on outdated data with limited observation periods and does not take into account mortality improvement. In this article, we propose a transparent and dynamic framework for modeling coupled lifetime dependence caused by both marital status and common mortality improvement factors. Dependence due to marital status is captured by a semi-Markov joint life model. Dependence due to common mortality improvement, which represents the correlation between mortality improvement patterns of coupled lives, is incorporated by a two-population mortality improvement model. The proposed model is applied to pricing the longevity risk in last survivor annuities sold in the United States and the United Kingdom.

Date: 2019
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DOI: 10.1080/10920277.2018.1513370

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