On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

Abstract

This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company's portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company's pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount 1 c and when they are in the second class, the premium paid is a constant amount 2 c such that 1 2 c c > . The nature of claims (low or high) is measured via random thresholds { } , 1, 2, i i Θ =  . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula.