Designing and valuing new equity-linked insurance products for couples

Equity-linked insurance products have gained popularity in recent years as retirement products with investment benefits. However, the design and pricing of these products for couples have been overlooked despite empirical evidence showing positive dependence in a couple's lifetimes. In this paper, we propose some suitable products for couples where the benefits depend on the death times of both lives, and perform valuation using the discounted density approach while allowing the lifetimes to be dependent. By modeling the lifetimes with a bivariate mixed Erlang distribution, closed-form pricing formulas are developed for a variety of benefit types such as income protection for the last survivor (possibly with roll-up guarantee or benefit indexation) and dynamic fund protection/withdrawals. Fitting of bivariate lifetime data is also discussed in relation to bivariate Laguerre series. The impact of dependence on the prices of these products is demonstrated via numerical examples. In particular, our results suggest that incorrectly assuming independence between lifetimes would overprice these products compared to the actual situation of positive dependence, thereby making the products less attractive.