Ruin Probability For A Classes Of Correlated Risk Processes With Negative Risk Sums

In this paper, we consider the correlated risk processes with negative risk sums. We define the correlation between the two classes of insurance business as the thinning dependence structure. We mainly study how the dependence between the two classes impacts on the ruin probability. In the first part of this paper, we introduce the background of this problem and give the model. In the second part, we study the ruin probability of this model and how the dependence of the two classes impacts on the ruin probability. In the third part, we give the numerical illustration of the ruin probability when the"claims"distributions are two exponential distributions. The research methods are: using the conditional probability theory to work out the moment generating function of process S(t) and its distribution function; using the increasing and declining character and the convexity to compare the Lundberg Exponent and the ruin probability of different processes. The main conclusions are: the ruin probability of the risk process is increasing according to the relativity of the classes; and with the initial surplus increasing, the influence of the relativity to the ruin probability is increasing.