Adverse selection in the annuity market when payoffs vary over the time of retirement

This study deals with a specific implication of adverse selection for annuity pricing. Varying the time path of the payoffs over the retirement periods affects the annuity demand and welfare of individuals with low and with high life expectancy in different ways. Therefore they can be separated by insurance firms through appropriate contract offers. We show that in this framework a Nash-Cournot equilibrium may not exist; if one exists, it will be a separating equilibrium. On the other hand, even if a separating equilibrium does not exist, a Wilson pooling equilibrium exists.