The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

Abstract EN

We consider a compound Poisson risk model with dependence and a constant dividend barrier.

A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula.

An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived.

We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.