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

Maria-Laura Torrente ()
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Maria-Laura Torrente: Università di Genova

Decisions in Economics and Finance, 2023, vol. 46, issue 2, No 11, 633 pages

Abstract: 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.

Keywords: Proportional reinsurance; Excess-of-loss reinsurance; Hamilton–Jacobi–Bellman equation; Stochastic control; Karush–Kuhn–Tucker conditions; 93E20; 91B30; 60J75 (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10203-023-00398-x

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