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Stochastic Pareto-optimal reinsurance policies. (English) Zbl 1290.91104

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91A80 Applications of game theory
91A12 Cooperative games
91A15 Stochastic games, stochastic differential games
93E20 Optimal stochastic control
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References:

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