On the ruin probability for the Cox correlated risk model perturbed by diffusion

In this paper we consider the Cox correlated risk model perturbed by a diffusion (Wiener) process. We first derive an analog of the Bernstein–Kolmogorov inequality for the probabilities of large deviations of Cox random sums. Then an exponential upper-bound which deals with the estimate of ruin probability based on the above inequality is proposed. In addition, several numerical examples are given to illustrate the theorem.