Modelling Joint Lifetimes of Couples by Using Bivariate Phase-type Distribution

Many insurance products and pension plans provide benefits which are related to couples, and thus under influence of the survival status of two lives. Some studies show the future lifetime of couples is correlated. Three reasons are available to confirm this fact: (1) catastrophe events that affect both lives, (2) the impact of spousal death and (3) the long-term association due to common life style. Regardless of these reasons, this dependence could have a financial impact on insurance companies and pension plans providers. In this article, we use a health index called physiological age to require a model based on Markov process that reflects reasons of impacts. Under this model, future joint life time of couples follow a bivariate phase-type distribution (BPH). The model has physical interpretation and closed-form expressions for some quantities and tractable computation for other ones. We use the model to pricing some products, relevant to couples annuities and life insurances, to show the effect of dependence on pricing.