The Gerber-Shiu Discounted Penalty Function For Several Different Risk Processes

After being introduced into ruin probability by Gerber and Shiu (1998), the Gerber-Shiu discounted penalty function has been become study focus of many scholars for morethan a decade because of its wide applications. We summarize some works of people inthis area, and will build several new models, then make investigations of their Gerber-Shiu functions.This paper’s innovation mainly has three points:By modifying the traditional Erlang(2) process through adding another kind ofclaims, we build a new model. We derive its system of integro-diferential equa-tions and solve it explicitly when the claims follow exponential distribution.We develop a model by introducing n claims beyond the traditional risk, then deriveits system of integro-diferential equations and the explicit expression of its Laplacetransform.We consider a risk model in which each main claim induces a delayed claim calleda by-claim. We develop a recursion method to explore its solution.