Research on Ruin Problems with Two-type by-claims and Delay Period Based on Compound Binomial Risk Model

In this paper, we propose a new a new risk model with two-type by-claims and delay period based on compound binomial distribution, in which every main claim induces two kinds of by-claims but either of the by-claims maybe delayed to the next period. The nature of the risk model with time-correlated claims is studied based on recursion of joint distribution functions. Through introducing three submodels, we obtain the expression of the joint distribution f(ux y) of the surplus just before ruin and deficit at ruin when initial surplus is 0 and the recursive formula of the joint distribution when initial surplus is u. In addition, when initial surplus is 0 the ruin probability of the risk model is given. At last, we provide the method to compute the ruin probability when initial surplus is u.