Minimal ruin probabilities and investment under interest force for a class of subexponential distributions

Peter Grandits

Scandinavian Actuarial Journal, 2005, vol. 2005, issue 6, 401-416

Abstract: We consider the infinite-time ruin probability of an insurance company investing in the stock market. This is done under the following assumptions: For the claim surplus process we use the classical Cramér-Lundberg model, where the claims have a distribution function, belonging to certain subclasses of the class of subexponential distributions. The stock price movement is modeled by geometric Brownian motion, and we allow positive interest rates for the riskless bond. In this setting we analyze the Hamilton-Jacobi-Bellman equation for the minimal ruin probability. We give asymptotic expressions for the minimal ruin probability, as well as for the optimal investment strategy. It turns out that the asymptotic order of the minimal ruin probability is different from the previous considered case of zero interest on the bond.

Date: 2005
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DOI: 10.1080/03461230500215479

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