Modeling of an insurance system and its large deviations analysis

We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R2R2. The claim sizes {Xi}{Xi} are an iid sequence with light tails. The interarrival times {τi}{τi} between claims are also iid and exponentially distributed. There is a fixed premium rate c1c1 that the customers pay; c