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August 2002 On minimizing the ruin probability by investment and reinsurance
Hanspeter Schmidli
Ann. Appl. Probab. 12(3): 890-907 (August 2002). DOI: 10.1214/aoap/1031863173

Abstract

We consider a classical risk model and allow investment into a risky asset modelled as a Black--Scholes model as well as (proportional) reinsurance. Via the Hamilton--Jacobi--Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation. We prove a verification theorem in order to show that any increasing solution to the HJB equation is bounded and solves the optimisation problem. We prove that an increasing solution to the HJB equation exists. Finally two numerical examples are discussed.

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Hanspeter Schmidli. "On minimizing the ruin probability by investment and reinsurance." Ann. Appl. Probab. 12 (3) 890 - 907, August 2002. https://doi.org/10.1214/aoap/1031863173

Information

Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1021.60061
MathSciNet: MR1925444
Digital Object Identifier: 10.1214/aoap/1031863173

Subjects:
Primary: 93E20
Secondary: 60G99, 91B30

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 3 • August 2002
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