Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model

Eisenberg J, Fabrykowski L, Schmeck MD (2021)
Risks 9(4): 73.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
OA 747.01 KB
Autor*in
Eisenberg, Julia; Fabrykowski, Lukas; Schmeck, Maren DianeUniBi
Abstract / Bemerkung
In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuous-time Markov chain with two states. The presence of regime-switching substantially complicates the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first- and second-order derivatives. Via Ito’s formula, we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation.
Erscheinungsjahr
2021
Zeitschriftentitel
Risks
Band
9
Ausgabe
4
Art.-Nr.
73
eISSN
2227-9091
Page URI
https://pub.uni-bielefeld.de/record/2954953

Zitieren

Eisenberg J, Fabrykowski L, Schmeck MD. Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks. 2021;9(4): 73.
Eisenberg, J., Fabrykowski, L., & Schmeck, M. D. (2021). Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks, 9(4), 73. https://doi.org/10.3390/risks9040073
Eisenberg, J., Fabrykowski, L., and Schmeck, M. D. (2021). Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks 9:73.
Eisenberg, J., Fabrykowski, L., & Schmeck, M.D., 2021. Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks, 9(4): 73.
J. Eisenberg, L. Fabrykowski, and M.D. Schmeck, “Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model”, Risks, vol. 9, 2021, : 73.
Eisenberg, J., Fabrykowski, L., Schmeck, M.D.: Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Risks. 9, : 73 (2021).
Eisenberg, Julia, Fabrykowski, Lukas, and Schmeck, Maren Diane. “Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model”. Risks 9.4 (2021): 73.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0):
Volltext(e)
Access Level
OA Open Access
Zuletzt Hochgeladen
2021-05-20T13:15:34Z
MD5 Prüfsumme
e8ca300c9f3b343953df520964878592

Material in PUB:
Frühere Version
Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model
Eisenberg J, Fabrykowski L, Schmeck MD (2021) Center for Mathematical Economics Working Papers; 648.
Bielefeld: Center for Mathematical Economics.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar