On a ruin problem for an insurance company investing reserves in the risky actives

In the classical Cramer-Lundberg model it is assumed that reserves are invested in constant cost actives. If the model parameters are such that the mean reserve increases then the ruin probability as a function of an initial capital is exponentially small. If reserves are invested in actives with geometric Brownian motion price dynamics then the situation is completely different. In the case of a small volatility the ruin probability decrease as a power function of an initial capital. But for a large volatility the ruin probability is 1. The talk contains the results on ruin probability asymptotics when the risky active price dynamics is a geometric Levy process. The proofs are based on recent results from the implicit renewal theory.