On a Decomposition of the Risk Ruin Probability Based on Fuzzy Markov Skeleton Process

According to the characteristics of risk model with perturbed by diffusion, a new kind of stochastic process- F-B process is proposed following from Fuzzy Markov Skeleton process. Then the ruin probabilities (caused by oscillation or by a claim) are discussed by F-B process. We derive a distribution of the ruin probability and a distribution of the surplus immediately before the time of ruin. Then continuous model and discrete model, risk model with compound Poisson process and risk model with double Poisson process, are used to illustrate the implementation of the model. Next limit theorems of two continuous risk models perturbed by diffusion are discussed. Finally simulation experiment is introduced.