The Ruin Probability Of Multiple Line Risk Model Perturbed By Diffusion

Risk theory, as a part of insurance or actuarial mathematics, deals with stochastic models of an insurance business and studies the probability of ruin. With continuously expanding of the risk operation's size form insurance companies, there is a limitation to the classical risk model and other generalized risk model.In this article, the author defines the model that premium income is a compound Poisson process, not a constant rate process, it is named compound Poisson process premium income risk model. Then in the process of compensation we use stochastic binomial sequence to make the risk model valuable. Finally we add risk process perturbed by diffusion to the model because insurance companies have indefinite income and payout. By the method of martingale, we prove the Lundberg inequality and formula on the ruin probability.