Ruin probabilities in the presence of regularly varying tails and optimal investment

We study the infinite time ruin probability in the classical Cramer-Lundberg model, where the company is allowed to invest their money in a stock, which is described by geometric Brownian motion. Starting from an integro-differential equation for the maximal survival probability, we analyze the case of claim sizes, which have distribution functions F with regularly varying tails. Our result is: if 1 - F is regularly varying with index rho < - 1, then the ruin probability Psi is also regularly varying with index rho < - 1. This holds under the assumption of zero interest rates. (C) 2002 Elsevier Science B.V. All rights reserved.