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Tom Boonen, University of Amsterdam; Wenjun, Jiang, University of Calgary
This paper studies an optimal reinsurance problem of Pareto-optimality when the contract is subject to default of the reinsurer. We assume that the reinsurer can invest a share of its wealth in a risky asset and default occurs when the reinsurer's end-of-period wealth is insufficient to cover the indemnity. We show that without the solvency regulation, the optimal indemnity function is of excess-of-loss form, regardless of the investment decision. We model solvency regulation as a constraint on the probability of default. Under solvency regulation, by assuming the investment decision remains the same as in the unconstrained solution, the optimal indemnity function is derived element-wisely. Partial results are given when the indemnity function and investment decision are jointly constrained by the solvency regulation. Numerical examples are provided to illustrate the implications of our results and the sensitivity of the solutions to the model parameters.
