Integro-differential Equations for a Class of Delayed Renewal Risk Processes with Dependence
Shiyu Song *
School of Mathematics, Liaoning Normal University, Dalian 116029, China.
*Author to whom correspondence should be addressed.
Abstract
The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. In (Willmot 2004), special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. In this paper, we consider a class of delayed and perturbed risk model with dependence between interclaim arrivals and claim sizes. The integro-differential equations for the Gerber-Shiu discounted penalty functions are derived.
Keywords: Gerber-Shiu discounted penalty function, delayed renewal risk process, multi-dependence events, Integro-differential equation