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Worst-case-optimal dynamic reinsurance for large claims

Korn, Ralf and Menkens, Olaf and Steffensen, Mogens (2012) Worst-case-optimal dynamic reinsurance for large claims. European Actuarial Journal, 2 (1). pp. 21-48. ISSN 2190-9733

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Abstract

We control the surplus process of a non-life insurance company by dynamic proportional reinsurance. The objective is to maximize expected (utility of the) surplus under the worst-case claim development. In the large claim case with a worst-case upper limit on claim numbers and claim sizes, we find the optimal reinsurance strategy in a differential game setting where the insurance company plays against mother nature. We analyze the resulting strategy and illustrate its characteristics numerically. A crucial feature of our result is that the optimal strategy is robust to claim number and size modeling and robust to the choice of utility function. This robustness makes a strong case for our approach. Numerical examples illustrate the characteristics of the new approach. We analyze the optimal strategy, e.g. in terms of the more conventional, in the insurance context, objective of minimizing the probability of ruin. Finally, we calculate the intrinsic risk-free return of the model and we show that the principle of Markowitz - don't put all your eggs in one basket - does not hold in this setting.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:dynamic proportional reinsurance; reserve process; worst-case scenario approach; Cramer-Lundberg model; differential game; robust optimization
Subjects:Mathematics > Economics, Mathematical
Mathematics > Mathematical models
Mathematics > Probabilities
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:Springer
Official URL:http://dx.doi.org/10.1007/s13385-012-0050-8
Copyright Information:© 2012 Springer The original publication is available at www.springerlink.com
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:17168
Deposited On:15 Aug 2012 14:07 by Olaf Menkens. Last Modified 15 Aug 2012 14:07

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