张爱丽, 刘章. 带两步保费率的复合Poisson风险模型的占位时[J]. 应用概率统计, 2020, 36(3): 261-276. DOI: 10.3969/j.issn.1001-4268.2020.03.004
引用本文: 张爱丽, 刘章. 带两步保费率的复合Poisson风险模型的占位时[J]. 应用概率统计, 2020, 36(3): 261-276. DOI: 10.3969/j.issn.1001-4268.2020.03.004
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ZHANG Aili, LIU Zhang. On Occupation Times for Compound Poisson Risk Model with Two-Step Premium Rate[J]. Chinese Journal of Applied Probability and Statistics, 2020, 36(3): 261-276. DOI: 10.3969/j.issn.1001-4268.2020.03.004
Citation: ZHANG Aili, LIU Zhang. On Occupation Times for Compound Poisson Risk Model with Two-Step Premium Rate[J]. Chinese Journal of Applied Probability and Statistics, 2020, 36(3): 261-276. DOI: 10.3969/j.issn.1001-4268.2020.03.004
shu

带两步保费率的复合Poisson风险模型的占位时

On Occupation Times for Compound Poisson Risk Model with Two-Step Premium Rate

    摘要
  • 摘要: 本文考虑了带两步保费率的经典复合Poisson风险模型. 使用一种替代方法,找到了两个不相交时间间隔的联合占位时对应Laplace变换的显式表达式.其中, Laplace变换用L\'evy过程的尺度函数来表示.

     

    Abstract: In this paper, we consider the classical compound Poisson risk model with two-step premium rate. Using an alternative approach, we find the explicit expressions for the Laplace transforms of joint occupation times over disjoint intervals for this model. The Laplace transforms are expressed in terms of scale functions of L\'evy processes.

     

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