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Optimal Dynamic XL Reinsurance

Published online by Cambridge University Press:  17 April 2015

Christian Hipp  and
Michael Vogt
Christian Hipp
Affiliation:
University of Karlsruhe, Germany
Michael Vogt
Affiliation:
University of Karlsruhe, Germany
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Abstract

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We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

Keywords

Stochastic controlRuin probabilityXL reinsurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 193 - 207
Copyright
Copyright © ASTIN Bulletin 2003

References

Grandell, J. (1991) Aspects of Risk Theory. Springer.CrossRefGoogle Scholar
Hipp, C. and Taksar, M. (2000) Stochastic Control for Optimal New Business. Insurance: Mathematics and Economics 26, 185–192.Google Scholar
Hipp, C. and Plum, M. (2000) Optimal Investment for Insurers. Insurance, Mathematics and Economics 27, 215–228.CrossRefGoogle Scholar
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1998) Stochastic Processes for Insurance and Finance. Wiley Series in Probability and Statistics 15.Google Scholar
Schäl, M. (1998) On piecewise deterministic Markov control processes: Control of jumps and of risk processes in insurance. Insurance: Mathematics and Economics 22, 75–91.Google Scholar
Schmidli, H. (2000) Optimal Proportional Reinsurance Policies in a Dynamic Setting. Research Report 403, Dept. Theor. Statis, Arhus University. 16.Google Scholar
Vogt, M. (2003) Optimale dynamische Ruckversicherung – ein Kontrolltheoretischer Ansatz. Dissertation, Universität Karlsruhe (TH).Google Scholar