Abstract
In this paper, we focus on the perturbed risk model with dependent relation and consider the relevance from two aspects. For one side, we use copula function to model the structure of the claim size and interclaim time, and on the other side, we establish the change of premium rat depending on the random thresholds. At last, we obtain the Integro-differential equations and its Laplace transforms of the Gerber-Shiu functions for the new risk model.
Highlights
Before a hundred years ago, the Lundberg-Cram’er classical model laid the foundation for ruin theory
We focus on the perturbed risk model with dependent relation and consider the relevance from two aspects
We use copula function to model the structure of the claim size and interclaim time, and on the other side, we establish the change of premium rat depending on the random thresholds
Summary
Before a hundred years ago, the Lundberg-Cram’er classical model laid the foundation for ruin theory. Gerber and Shiu put forward a classical function called the Gerber-Shiu expected discounted penalty functions to study ruin probability better, and they use the Brownian motion to be the perturbation term for the first time. Since the compound Poisson risk model perturbed (1.3) and EDP function were proposed, it has received a lot of attention, and the EDP function has been studied fully (including the equation of integro-differential, the Laplace transform, analytic solutions, etc.), see e.g. Zhou and Cai [15] analyze the dependence structure between the premium rate and the claim size for model (1.3). It doesn’t consider the dependence of interclaim time and claim size.
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