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Ruin Probability for the Compound Mixed Poisson Risk Model

Miao Bai

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Abstract

The compound mixed Poisson risk model with perturb at ion is introduced in the present paper and the asympototics of ruin probability is obtained when the claim size distributions are light tailed. It is proved th at the ruin probability increases in the variance of the Wiener process. An examp le is given to show that the present model is more delicate than the risk model introduced by Dufresne and Gerber (Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Mathematics and Economics, 1991, 10, 51～59)

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What this paper is about

The compound mixed Poisson risk model with perturb at ion is introduced in the present paper and the asympototics of ruin probability is obtained when the claim size distributions are light tailed. It is proved th at the ruin probability increases in the variance of the Wiener process. An examp le is given to show that the present model is more delicate than the risk model introduced by Dufresne and Gerber (Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Mathematics and Economics, 1991, 10, 51～59)

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Available abstract

The compound mixed Poisson risk model with perturb at ion is introduced in the present paper and the asympototics of ruin probability is obtained when the claim size distributions are light tailed. It is proved th at the ruin probability increases in the variance of the Wiener process. An examp le is given to show that the present model is more delicate than the risk model introduced by Dufresne and Gerber (Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Mathematics and Economics, 1991, 10, 51～59)

Key concepts: Zero-inflated model, Poisson distribution, Compound Poisson process, Ruin theory, Risk model, Mathematics, Poisson regression, Cox process

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