| 摘要: |
| 相位分布是定义为某个马氏跳过程吸收时间的分布，它在正半轴上形成了一类可以在普遍性与易处理之间的平衡点，任何正的分布都可以由相位分布无限接近；在带常利率的时间间隔为相位分布的更新风险模型下，用概率方法得出了相位分布的一些基本性质及Gerber Shiu折现罚金函数的确切解. |
| 关键词: 相位分布更新风险模型 Gerber Shiu折现罚金函数 破产时刻 破产前瞬时盈余额 赤字 |
| DOI： |
| 分类号: |
| 基金项目: |
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| The Gerber Shiu Discounted Penalty Function by Probabilistic Methods |
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XIAO Ju Xia， SHI Jian Hong
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| Abstract: |
| Phase type distributions， defined as the distribution of absorption times of certain Markov jump processes， constitute a class of distribution on the positive real axis which seems to strike a balance between generality and tractability.Any positive distribution can be approximated arbitrarily by phase type distributions.Under the condition that the inter claim times of constant interest is phase type distribution risk model， some of their basic properties and the precise solution of Gerber Shiu discounted penalty function are obtained. |
| Key words: the phase type inter claim times Gerber Shiu discounted penalty function time o f ruin surplus immediately before ruin deficit |
