Non-concave expected utility optimization with uncertain time horizon: an application to participating life insurance contracts

We examine an expected utility maximization problem with an uncertain time horizon, a classical example being a life insurance contract due at the time of death. Life insurance contracts usually have an option-like form leading to a non-concave optimization problem. We consider general utility functions and give necessary and sufficient optimality conditions, deriving a computationally tractable algorithm. A numerical study is done to illustrate our findings. Our analysis suggests that the possible occurrence of a premature stopping leads to a reduced performance of the optimal portfolio compared to a setting without time-horizon uncertainty.