Stochastic analysis of longevity risk in dependent multiple life annuities

Abstract

The aim of this paper is to examine the n et single premiums of multiple l ife annuities using stochastic rates of return and dynamic life table under the assumption of dependency of spouses’ future lifetimes. In order to calculate the present value of the annuity or the net single premium, two parameters are needed: survival rate and the rate of return. For the survival rates, we used a life table with a time dimension for Turkey, in which mortality rates follow a declining pattern, a major indicator of longevity. For the rate of return, two portfolios were created, low and high risk portfolios that include assets with different ratios and AR(1) process was used to model the rates of return based on both portfolios. To assess the dependency, future lifetimes of spouses were assumed to follow Frank’s copula model. The effects of longevity, stochastic rates of return and dependency of future lifetimes on these net single premiums were analyzed.