Projects per year
Abstract
Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber–Shiu functions)in a Cramér–Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modeled as time dependent control functions, which lead to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton–Jacobi–Bellman equation. We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.
Original language | English |
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Pages (from-to) | 82-91 |
Number of pages | 10 |
Journal | Insurance / Mathematics & economics |
Volume | 87 |
Issue number | 87 |
Early online date | Apr 2019 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Cramér-Lundberg model
- Dynamic reinsurance
- Gerber–Shiu functions
- Optimal stochastic control
- Policy iteration
ASJC Scopus subject areas
- Economics and Econometrics
- Statistics and Probability
- Statistics, Probability and Uncertainty
Fields of Expertise
- Information, Communication & Computing
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Projects
- 1 Active
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Special Research Area (SFB) F55 Quasi-Monte Carlo Methods: Theory and Applications
Grabner, P., Tichy, R., Kusner, W. B., Ziefle, J., Brauchart, J., Iaco, M. R. & Aistleitner, C.
1/02/14 → 31/01/22
Project: Research project
Activities
- 1 Talk at conference or symposium
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Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model
Stefan Michael Thonhauser (Speaker)11 Jul 2019Activity: Talk or presentation › Talk at conference or symposium › Science to science