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Optimal proportional and excess-of-loss reinsurance for multiple classes of insurance business

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  • Maria-Laura Torrente

    (Università di Genova)

Abstract

In this paper we consider a reinsurance strategy which combines a proportional and an excess-of-loss reinsurance in a risk model with multiple dependent classes of insurance business. Under the assumption that the claim number of the classes has a multivariate Poisson distribution, the aim is to maximize the expected utility of terminal wealth. In a general setting, after deriving the corresponding Hamilton–Jacobi–Bellman equation, we prove a Verification Theorem and identify sufficient conditions for the optimality. Then, in a special case with exponential utility, an explicit solution is found by solving an intricate associated static constrained optimization problem.

Suggested Citation

  • Maria-Laura Torrente, 2023. "Optimal proportional and excess-of-loss reinsurance for multiple classes of insurance business," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 611-633, December.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:2:d:10.1007_s10203-023-00398-x
    DOI: 10.1007/s10203-023-00398-x
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    More about this item

    Keywords

    Proportional reinsurance; Excess-of-loss reinsurance; Hamilton–Jacobi–Bellman equation; Stochastic control; Karush–Kuhn–Tucker conditions;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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