Two-dimensional Risk Model With Thinning Dependent Structure

Ruin theory under multivariate risk models is difficult. In this paper, we propose a two-dimensional risk model with thinning dependent structure and three different types of ruin probabilities are defined. General explicit expression for this multivariate ruin probability is not easy to obtain. In this paper, we investigate some analytic properties and the bounds for the ruin probabilities.This paper includes five chapters. The first chapter is the introduction. In the second chapter, we introduce the background of the risk process, the two-dimensional risk model with thinning dependent structure and three different types of ruin probabilities. In the third chapter, we obtain an integral equation for the ruin probability and an integral-differential equation for the survival probability. In the fourth chapter, we derive some bounds of the ruin probabilities. The last chapter gives a conclusion for the main results of the paper.