The Annals of Applied Probability

On minimizing the ruin probability by investment and reinsurance

Hanspeter Schmidli

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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

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

First available in Project Euclid: 12 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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