Open Access
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


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.


Download Citation

Hanspeter Schmidli. "On minimizing the ruin probability by investment and reinsurance." Ann. Appl. Probab. 12 (3) 890 - 907, August 2002.


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

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

Primary: 93E20
Secondary: 60G99 , 91B30

Keywords: Black--Scholes model , Hamilton--Jacobi--Bellman equation , optimal control , reinsurance , ruin probability , Stochastic control

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
Back to Top