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

Author

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  • Matteo Brachetta

    (Department of Economics, University of Chieti-Pescara, 42-65127 Pescara, Italy
    Current address: Viale Pindaro, 42-65127 Pescara, Italy.
    These authors contributed equally to this work.)

  • Claudia Ceci

    (Department of Economics, University of Chieti-Pescara, 42-65127 Pescara, Italy
    Current address: Viale Pindaro, 42-65127 Pescara, Italy.
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Matteo Brachetta & Claudia Ceci, 2019. "Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models," Risks, MDPI, vol. 7(2), pages 1-23, May.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:48-:d:227464
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    References listed on IDEAS

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    1. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
    2. Claudia Ceci, 2012. "Utility Maximization With Intermediate Consumption Under Restricted Information For Jump Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-34.
    3. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    4. Meng, Hui & Zhang, Xin, 2010. "Optimal Risk Control for The Excess of Loss Reinsurance Policies," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 179-197, May.
    5. Xin Zhang & Ming Zhou & Junyi Guo, 2007. "Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 63-71, January.
    6. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    7. Claudia Ceci & Anna Gerardi, 2006. "A Model For High Frequency Data Under Partial Information: A Filtering Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 555-576.
    8. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    9. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
    10. Brachetta, M. & Ceci, C., 2019. "Optimal proportional reinsurance and investment for stochastic factor models," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 15-33.
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    Cited by:

    1. Matteo Brachetta & Hanspeter Schmidli, 2020. "Optimal reinsurance and investment in a diffusion model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 341-361, June.
    2. Matteo Brachetta & Claudia Ceci, 2021. "Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences," Mathematics, MDPI, vol. 9(4), pages 1-20, February.
    3. Brachetta, M. & Ceci, C., 2020. "A BSDE-based approach for the optimal reinsurance problem under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 1-16.
    4. Matteo Brachetta & Claudia Ceci, 2019. "A BSDE-based approach for the optimal reinsurance problem under partial information," Papers 1910.05999, arXiv.org, revised May 2020.
    5. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2021. "Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets," Papers 2105.07524, arXiv.org.

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