A deductible claim process risk model and ruin probability

This paper studies a deductible claim process risk model. The author puts an emphasis on studying the risk model under the condition that claim number process is Poisson process and loss distribution is exponential distribution. According to the calculation, draw the interesting conclusion that under the two situations whether regard deductible as claim or not, the aggregate claim is the same. Furthermore, depending on the conclusion in classical risk models draw the expression of relative security loading, adjustment coefficient, and ruin probability. Finally, the author using renewal function and relative conclusion draw the explicit expression of ruin probability in this risk model.