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.
| Translated title of the contribution | Optimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model |
|---|---|
| Original language | English |
| 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 |
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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
Cite this
Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model. / Preischl, Michael Julius; Thonhauser, Stefan.
In: Insurance / Mathematics & economics, Vol. 87, No. 87, 2019, p. 82-91.Research output: Contribution to journal › Article › Research › peer-review
}
TY - JOUR
T1 - Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model
AU - Preischl, Michael Julius
AU - Thonhauser, Stefan
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Cramér-Lundberg model
KW - Dynamic reinsurance
KW - Gerber–Shiu functions
KW - Optimal stochastic control
KW - Policy iteration
UR - http://www.scopus.com/inward/record.url?scp=85064859764&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.insmatheco.2019.04.002
DO - https://doi.org/10.1016/j.insmatheco.2019.04.002
M3 - Article
VL - 87
SP - 82
EP - 91
JO - Insurance / Mathematics & economics
JF - Insurance / Mathematics & economics
SN - 0167-6687
IS - 87
ER -