In this paper, we focus on the perturbed risk model with dependent relation\nand consider the relevance from two aspects. For one side, we use copula\nfunction to model the structure of the claim size and interclaim time, and on\nthe other side, we establish the change of premium rat depending on the\nrandom thresholds. At last, we obtain the Integro-differential equations and\nits Laplace transforms of the Gerber-Shiu functions for the new risk model.
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