Optimal hedging of demographic risk in life insurance
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A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic–demographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First, how can an insurer optimally hedge environmental risk by trading in a given set of derivatives? Second, assuming that insurers perform optimal hedging strategies in a given derivatives market, how can the very derivatives be designed in order to minimize the average hedging error across a given population of insurers? The paper comes with the caveat emptor that the theory will find its prime applications, not in securitization of longevity risk, but rather in securitization of catastrophic mortality risk.
KeywordsStochastic mortality Mortality derivatives Mean-variance hedging Optimal design of derivatives
Mathematics Subject Classification60G55 62P05 91B30 91G20
JEL ClassificationC02 G11
The author thanks the BNP Paribas Insurance Chair “Management de la modélisation” for financial support. The views expressed in this document are the author’s own and do not necessarily reflect those endorsed by BNP Paribas Insurance. Thanks are also due to referees and editors whose general comments as well as attention to details were helpful.
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