On an Erlang(2) Process with Dependence Structure between Interclaim Arrivals and Claim Sizes
Qiao Li *
School of Mathematics, Liaoning Normal University, Dalian, China.
Zhenhua Bao
School of Mathematics, Liaoning Normal University, Dalian, China.
*Author to whom correspondence should be addressed.
Abstract
This paper considers an extension to the classical compound Poisson risk model for which an Erlang(2) process is utillized to the dependence structure between the claim sizes and interclaim times. In this framework, we derive the Lundberg generalised equation and the number of its roots, and the Laplace Transform(LT) of the expected discounted penalty function. We also show that the Gerber-Shiu function satisfies a defective renewal equation. Some explicit expressions are given to measure the impact of Erlang(2) dependence structure in the risk model on the ruin probability.
Keywords: Dependence, Gerber-Shiu penalty function, Laplace Transform, defective renewal equation, ruin probability