Ruin Probability Searched By Differential Equation

In this article, we intend to give the exact compute of the ruin probability. We get a more general risk model based on one driven by a compound Poisson process is firstly investigated. We extend the study in (Li.,2009) to incorporate parameter e(x) to denote a surplus-dependent expense ratio function in the model. It is investigated as another case that both the force of interest and tax rate are surplus-dependent, meanwhile the claims are exponential. We further introduce the differential equation method and demonstrate the differential equation of the ruin probability with the mixed-exponential claims and a constant parameterδ-interest rate. Finally some numerical results are illustrated.