The Annals of Applied Probability

On minimizing the ruin probability by investment and reinsurance

Hanspeter Schmidli

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 12, Number 3 (2002), 890-907.

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1031863173

Digital Object Identifier
doi:10.1214/aoap/1031863173

Mathematical Reviews number (MathSciNet)
MR1925444

Zentralblatt MATH identifier
1021.60061

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 60G99: None of the above, but in this section 91B30: Risk theory, insurance

Keywords
Optimal control stochastic control ruin probability Hamilton--Jacobi--Bellman equation Black--Scholes model reinsurance

Citation

Schmidli, Hanspeter. On minimizing the ruin probability by investment and reinsurance. Ann. Appl. Probab. 12 (2002), no. 3, 890--907. doi:10.1214/aoap/1031863173. https://projecteuclid.org/euclid.aoap/1031863173


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