Ruin Probability In The Presence Of Risky Investments

It is well known that the analysis of activity of an insurance company in conditions of uncertainty is of great importance. Starting from the classical papers of Cramer and Lundberg which first considered the ruin problem in stochastic environment, this subject has attracted much attention. Recall that, in the classical Cramer - Lundberg model satisfying the Cramer condition and, the positive safety loading assumption, the ruin probability as a function of the initial endowment decreases exponentially.