On minimizing the ruin probability by investment and reinsurance. (English) Zbl 1021.60061

Schmidli, Hanspeter

Ann. Appl. Probab. 12, No. 3, 890-907 (2002).

The author considers a risk model in which the insurance company is allowed to invest in a risky asset as well as to take (proportional) reinsurance. By using the Hamilton-Jacobi-Bellman approach, the author finds a candidate for the optimal strategy and develops a numerical procedure to solve the HJB equation. The author shows that the HJB equation admits an increasing solution and that any increasing solution to the HJB equation is bounded and solves the optimization problem.

Reviewer: Renming Song (Urbana)

MSC:

60J65	Brownian motion
91B30	Risk theory, insurance (MSC2010)
60G44	Martingales with continuous parameter

Keywords:

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