Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence

Abstract

This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized mixed equilibrium distribution, we derive the integro-differential Equations of the Gerber−Shiu function and its defective renewal equations. For the situation where claim amounts follow exponential distribution, we provide an explicit expression of the Gerber−Shiu function. Numerical examples are provided to illustrate the ruin probability.

Keywords

• ruin theory
• delay renewal risk process
• renewal equation
• convolution formula
• diffusion process
• fgm copula
• exponential and equilibrium distribution.