2023 Australasian Actuarial Education and Research Symposium

Kelvin Tang

University of New South Wales

Valuing equity-linked insurance products for couples

This is joint work with Eric Cheung, Jae Kyung Woo

In the pricing of joint life contracts, it is often convenient to assume that the lifetimes of different persons are independent. However, some results in the literature have demonstrated that the lifetimes of a couple typically exhibit positive dependence, and failure to account for this dependence can lead to significant mispricing of benefits. In this presentation, we explore the valuation of some equity-linked products for a couple under the assumption that the lifetimes can be dependent. While traditional equity-linked products are usually only defined for a single life, we propose some products designed specifically for a couple where the benefit can depend on the death times of both lives. These include, for example, a reversionary annuity that pays the surviving spouse until his/her death, where the payment can depend on an underlying equity index which helps to guarantee the standard of living for the surviving spouse. By modelling the joint mortality function with a bivariate mixed Erlang distribution, our model generalises some existing results in the literature and finds closed-form solutions for the expected value of the products. In principle, our results can also be generalised to model multiple dependent events.