Stochastic Pareto-optimal reinsurance policies

We model reinsurance as a stochastic cooperation game in a continuous-time framework. Employing stochastic control theory and dynamic programming techniques, we study Pareto-optimal solutions to the game and derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation. After analyzing the HJB equation, we show that the Pareto-optimal policies may be classified into either unlimited excess of loss functions or proportional functions based on different premium share principles. To illustrate our results, we solve several examples for explicit solutions.