Ruin Probability For The Risk Process With Correlated Negative Risk Sums

Ruin probability is a topic in ruin theory of risk models. Many workers have been interested in the Risk Process with Correlated Risk Sums. But the work that has been in references is about the Risk Process with Correlated Positive Risk Sums. In this paper, we consider the risk process with correlated negative risk sums. We study how the dependence between the classes impacts on the ruin probability. We compare the results with the risk model with independent classes. In the first part of this paper, we give the model and its backgroud. In the second part, we study the dependence between the two classes impacts on the ruin probability (Theorem 2.3.1). In the third part of this paper, We give the numerical illustration for the ruin probability when the " claims " distributions .are two exponential distributions or an exponential and a (2, ) distribution or two (2, ) distributions.