| Pricing of insurance contracts has generated much interest among researchers and practitioners in the last two decades. Rapid mortality decline in developed nations calls for methodologies that properly assess and price risks entailed in insurance contracts. To address this problem, we propose the use of two types of imperfect hedging techniques---quantile and efficient hedging. We show that they are effective tools for managing both financial and insurance risk elements inherent in equity-linked life insurance contracts. Financial risk comes from the volatility of the financial instruments underlying the contract, while insurance risk arises from the dependence of the payoff on the client's survival to maturity of the contract.;First, we introduce the two hedging methodologies and show why they are attractive for pricing of equity-linked life insurance contracts. We give explicit theoretical results for the price of a contract paying the maximum of two risky asset values at maturity, provided the contract buyer survives to this date. We also prove a result which allows straightforward generalization of our approach to payoffs with n risky assets. Using numerical examples, we demonstrate risk management possibilities for the seller of the contract and the advantages of applying quantile or efficient hedging. These methods are computationally inexpensive, intuitive, and flexible in terms of risk management yet precise in quantifying financial and insurance risks.;Next, we study modern mortality trends in the context of imperfect hedging. We analyze the classical mortality models of Gompertz and Makeham, and the recently developed approach of Lee and Carter for fitting and forecasting mortality. Thus we extend the topic of quantile and efficient hedging beyond financial mathematics into actuarial science. By performing a comparative study between the United States, Sweden and Japan, we show that mortality model selection carries significant implications for risk management in equity-linked life insurance. |
