An Estimation Of Ruin Probability For Compound Poisson Process Premium Income Risk Model

Collective risk theory as a part of insurance business, the compound Poisson risk theory is one of the principal models in the lengthy history of risk theory, many classical results have been got in many monograph, many scientists have generalized the classical compound Poisson risk model in many ways. But, in most of general risk model, the premium income is a constant rate, scholar have generalized the aggregated premium income from a constant rate process to a Poisson process.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 the model is simplified, the theory of martingale, simulation, and diffusion approximations are discussed firstly. These methods are applied in the model. Then get some useful results, so we can estimate the upper bound for the ruinprobability and the approximation of the finite time ruin probability. At the end of the paper an example is given.