关键词: 赤字分布, 强马氏性, 预警区间, 矩母函数

Abstract:

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.

Key words: Distribution of deficit, Strong Markovproperty, Duration of the negative surplus, Moment generating function