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Open AccessFeature PaperArticle

Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models

by Matteo Brachetta *,†,‡ and Claudia Ceci †,‡
Department of Economics, University of Chieti-Pescara, 42-65127 Pescara, Italy
*
Author to whom correspondence should be addressed.
Current address: Viale Pindaro, 42-65127 Pescara, Italy.
These authors contributed equally to this work.
Risks 2019, 7(2), 48; https://doi.org/10.3390/risks7020048
Received: 31 January 2019 / Revised: 18 April 2019 / Accepted: 26 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate r. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed. View Full-Text
Keywords: optimal reinsurance; excess-of-loss reinsurance; Hamilton-Jacobi-Bellman equation; stochastic factor model; stochastic control optimal reinsurance; excess-of-loss reinsurance; Hamilton-Jacobi-Bellman equation; stochastic factor model; stochastic control
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Brachetta, M.; Ceci, C. Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models. Risks 2019, 7, 48.

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