7. Discussion
In this paper, we consider a portfolio selection problem for a utility maximizing insurance company selling participating contracts. Relying on the martingale approach and the pointwise optimization technique, we are able to obtain a closed-form solution. In the pointwise optimization procedure we adopt a concavification technique to transform the problem to a solvable one. With the optimal solution, we present numerical examples as well as comparisons with the standard CPPI and OBPI strategies. Finally, we consider a constrained version of the optimization problem with bounded control, obtain the solution by employing a numerical method, and compare the solutions of the constrained and unconstrained problems.