一类推广的复合Poisson-Geometric风险模型下预警区问题的研究

The Analysis of the Duration of the Negative Surplus for a Generalized Compound Poisson-Geometric Risk Model

该文研究一类推广的复合Poisson-Geometric风险模型的预警区问题,此模型保费收入过程是复合Poisson过程,索赔次数过程是复合Poisson-Geometric过程.充分利用盈余过程的强马氏性和全期望公式,得到了赤字分布的积分表达式,进而得到了单个预警区和总体预警区的矩母函数的表达式.

This paper mainly studies a generalized compound Poisson-Geometric risk model in which the income of insurance premiums is a compound Poisson process and the number of claims is a compound Poisson-Geometric process. This risk model has practical applications in the insurance industry. In this paper, the authors focus on the duration of the negative surplus（DNS） under the above risk model. By taking full advantage of the strong Markov property of the surplus process and the total expectation formula, they derive the distribution of the deficit at ruin, and the moment generating functions of the DNS.