Bivariate analysis of survivorship and persistency

Voluntary non-payment of premiums leads to policy termination. When policies are terminated, it is costly to several parties of insurance contracts. These costs include the inability of the insurance company to recover acquisition expenses, loss of income from renewal premiums by the insurance agent, and the loss of premiums paid and insurance coverage by the contractholder. While most of these costs can be directly accounted for, there is the additional hidden cost resulting from mortality selection. This refers to the tendency of contractholders who are generally healthier to select against the insurance company by voluntarily terminating their policies. This paper explores a methodology to quantify the cost of mortality selection and to examine for the presence of such selection. While standard actuarial models of survivorship and persistency consist of specifying distributions for times until death and withdrawal, the typical assumption is that these random times are independent. We will use a more general approach of specifying the bivariate distributions using copulas for these random times without having to assume independence. We demonstrate procedures to estimate parameters in the model, and we show how one can use these estimates to predict more accurate future cash flows.