The Uncertain Force of Mortality Framework: Pricing Unit-Linked Life Insurance Contracts

Quant Talk
Wednesday, 02 December 2009
6.30 pm, room 20

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Abstract

Unit-linked life insurance contracts link the financial market and the insurance market together. In a complete and arbitrage-free financial market, financial risk can be hedged perfectly, but perfect hedging is not possible when mortality risk is embedded in a financial product. For many years, this problem was ignored by assuming that the force of mortality is deterministic. Under this assumption, an insurance company can hedge against mortality risk by pooling a large number of policyholders together. It then only needs to deal with the financial risk. However, in recent years it has been acknowledged that the force of mortality is actually stochastic and researchers have tried to model this stochastic process. The drawback of this procedure is that it cannot provide a nearly perfect hedge against mortality risk unless a large number of mortality-linked financial products are liquidly traded. In contrast to specifying a stochastic model for the force of mortality, we provide a framework where the force of mortality is uncertain but stays within lower and upper bounds. Within this framework, we obtain upper and lower price bounds for European-style unit-linked life insurance contracts by applying optimal control theory and PDE methods. In particular, the upper and lower price bounds are obtained by seeking out the worst and best scenarios for varying forces of mortality. The PDE formulation of the pricing problem is solved with finite difference methods. The upper and lower price bounds enable us to enhance hedging strategies and reduce exposure to financial and mortality risks.

The work is co-authored by Jing Li (Bonn Graduate School of Economics, University of Bonn).