| Summary: | 博士 === 國立政治大學 === 風險管理與保險研究所 === 104 === How to manage mortality rate risks is essential to the long-term solvency of life insurance companies. The literatures proposed to hedge the products subject to the longevity risk (such as annuities) by using the products subject to the mortality risk (e.g., whole life insurance) sold by an insurer. Such natural hedging is intuitive but may be difficult to implement due to the rigid sales market and incentive issues. We propose to embed natural hedging into product design so that the hedging may occur within a product. The key is to offset the impact of mortality on the timing of death that in turn determines the present value of the death benefit by cleverly choose the growth rate of the death benefit, the factor of “how much to pay” while δ would reflect the time value of payment. This article provides theoretical derivations, graphical illustrations, and numerical analyses of both life insurance products and annuity products to illustrate the idea of embedding natural hedging into product design.
In the first essay, we use actuarial methods to come up with the theoretical derivation of the optimal natural hedging strategy and we can easily embed it into insurance product design. In the second essay, furthermore, we evaluate the impact of uncertainty passed on by future mortality rate and interest rate against the product design based on the optimal natural hedging strategy. We use the numerical illustration and obtain the minimum risk or nearly no risk at all under the optimal strategy. We develop not only on the life insurance product design, in the third essay, we also progress the product design of annuity products.
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