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.

Diskussionspapier | Veröffentlicht | Englisch
 
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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 complicates substantially 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 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.

Classification: 60K10; 91B30; 60J65; 49K15
Stichworte
Reinsurance; Regime-switching; Brownian motion; Markov chain; Optimal control; HJB equation; Ordinary differential equations; Boundary value problem
Erscheinungsjahr
2021
Serientitel
Center for Mathematical Economics Working Papers
Band
648
Seite(n)
36
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2953603

Zitieren

Eisenberg J, Fabrykowski L, Schmeck MD. Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Center for Mathematical Economics Working Papers. Vol 648. Bielefeld: Center for Mathematical Economics; 2021.
Eisenberg, J., Fabrykowski, L., & Schmeck, M. D. (2021). Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model (Center for Mathematical Economics Working Papers, 648). Bielefeld: Center for Mathematical Economics.
Eisenberg, J., Fabrykowski, L., and Schmeck, M. D. (2021). Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Center for Mathematical Economics Working Papers, 648, Bielefeld: Center for Mathematical Economics.
Eisenberg, J., Fabrykowski, L., & Schmeck, M.D., 2021. Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model, Center for Mathematical Economics Working Papers, no.648, Bielefeld: Center for Mathematical Economics.
J. Eisenberg, L. Fabrykowski, and M.D. Schmeck, Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model, Center for Mathematical Economics Working Papers, vol. 648, Bielefeld: Center for Mathematical Economics, 2021.
Eisenberg, J., Fabrykowski, L., Schmeck, M.D.: Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Center for Mathematical Economics Working Papers, 648. Center for Mathematical Economics, Bielefeld (2021).
Eisenberg, Julia, Fabrykowski, Lukas, and Schmeck, Maren Diane. Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model. Bielefeld: Center for Mathematical Economics, 2021. Center for Mathematical Economics Working Papers. 648.
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2021-04-06T12:15:31Z
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Spätere Version
Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model
Eisenberg J, Fabrykowski L, Schmeck MD (2021)
Risks 9(4): 73.

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