Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Michael Julius Preischl; Stefan Thonhauser

doi:https://doi.org/10.1016/j.insmatheco.2019.04.002

Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Titel in Übersetzung: Optimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model

Michael Julius Preischl, Stefan Thonhauser

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Titel in Übersetzung	Optimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model
Originalsprache	englisch
Seiten (von - bis)	82-91
Seitenumfang	10
Fachzeitschrift	Insurance / Mathematics & economics
Jahrgang	87
Ausgabenummer	87
Frühes Online-Datum	Apr. 2019
DOIs	https://doi.org/10.1016/j.insmatheco.2019.04.002
Publikationsstatus	Veröffentlicht - 2019

ASJC Scopus subject areas

Volkswirtschaftslehre und Ökonometrie
Statistik und Wahrscheinlichkeit
Statistik, Wahrscheinlichkeit und Ungewissheit

Fields of Expertise

Information, Communication & Computing

Zugriff auf Dokument

https://doi.org/10.1016/j.insmatheco.2019.04.002

https://arxiv.org/pdf/1809.00990.pdf

Andere Dateien und Links

http://www.scopus.com/inward/record.url?scp=85064859764&partnerID=8YFLogxK

Spezialforschungsbereich (SFB) F55 Quasi-Monte Carlo Methoden: Theorie und Anwendungen
Grabner, P., Tichy, R., Kusner, W. B., Ziefle, J., Brauchart, J., Iaco, M. R. & Aistleitner, C.
1/02/14 → 31/01/23
Projekt: Forschungsprojekt

1 Vortrag bei Konferenz oder Fachtagung
1 Vortrag bei Workshop, Seminar oder Kurs

PDMP based risk models
Stefan Michael Thonhauser (Redner/in)
11 Dez. 2022
Aktivität: Vortrag oder Präsentation › Vortrag bei Workshop, Seminar oder Kurs › Science to science
Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model
Stefan Michael Thonhauser (Redner/in)
11 Juli 2019
Aktivität: Vortrag oder Präsentation › Vortrag bei Konferenz oder Fachtagung › Science to science

Dieses zitieren

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title = "Optimal reinsurance for Gerber–Shiu functions in the Cram{\'e}r–Lundberg model",

abstract = "Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber–Shiu functions)in a Cram{\'e}r–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.",

keywords = "Cram{\'e}r-Lundberg model, Dynamic reinsurance, Gerber–Shiu functions, Optimal stochastic control, Policy iteration",

author = "Preischl, {Michael Julius} and Stefan Thonhauser",

year = "2019",

doi = "https://doi.org/10.1016/j.insmatheco.2019.04.002",

language = "English",

volume = "87",

pages = "82--91",

journal = "Insurance / Mathematics & economics",

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AU - Preischl, Michael Julius

AU - Thonhauser, Stefan

PY - 2019

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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

IS - 87

ER -

Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Abstract

ASJC Scopus subject areas

Fields of Expertise

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Projekte

Spezialforschungsbereich (SFB) F55 Quasi-Monte Carlo Methoden: Theorie und Anwendungen

Aktivitäten

PDMP based risk models

Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model

Dieses zitieren