Application of linear relation model on mortality immunization
The prediction of future mortality rates by any existing mortality projection models is not precise, which causes an exposure to mortality and longevity risks for life insurance companies. Since a change in mortality rates has opposite impacts on the surpluses (negative reserves) of life insurance and annuity products, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this project, we develop a frame work of implementing non-size free duration and convexity matching strategies to hedge against mortality and longevity risks. We apply relational models to capture the mortality movements by assuming that the simulated mortality sequence is a proportional and/or a constant change of the expected one, and the amount of the changes varies in the length of the sequence. With the magnitude of the proportional and/or constant changes, we determine the optimal weights of allocating the life insurance and annuity products in a portfolio for mortality immunization according to each of the proposed duration and convexity matching strategies. Comparing the hedging performance of non-size free matching strategies with size free ones proposed by Lin and Tsai (2014), we demonstrate that non-size free duration and convexity matching strategies can hedge against mortality and longevity risks more effectively than the corresponding size free ones.
Keywords: relational model; longevity risk; mortality risk; mortality duration; mortality convexity; hedge effectiveness; surplus