Reinsurance For The Proportional Contract In Two-Dimentional Compound Poisson Model

Multi-dimentional risk model is very complex. In this paper we define two-dimentional compound Poisson model creatively. Apply the martingale approach of piecewise deterministic Markov process (PDMP) and the change of probability measure to the assumed model, then we obtain the explicit expressions of the ruin probability. Analyzing the adjustment coefficients the optimal proportional reinsurance contract in the two-dimentional compound Poisson model can be acquired. In order to make the further research, we define the retention function on the process, but not on the claim size. This is another creative opinion we put forward. At last, numerical examples are presented.This paper includes five chapters. In the first chapter, the relative background is given. We propose the new model and some hypotheses in the second part. The martingale approach of PDMP and the change of probability measure are embodied in the third chapter-the main body of the paper. By analyzing the correlation of the model the ruin probability and the reinsurance for the proportional contract are derived. In the fourth chapter numerical examples are given. Conclusion is the last part.