Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (2): 501-514.

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On the Analysis of Ruin-Related Quantities in the Nonhomogeneous Compound Poisson Risk Model

Yingchun Deng1,Man Li1,Ya Huang2,Jieming Zhou1,*()   

  1. 1 Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) & School of Mathematics and Statistics, Hunan Normal University, Changsha 410081
    2 School of Business, Hunan Normal University, Changsha 410081
  • Received:2018-12-24 Online:2020-04-26 Published:2020-05-21
  • Contact: Jieming Zhou E-mail:jmzhou@hunnu.edu.cn
  • Supported by:
    the Philosophy and Social Science Fund of Hunan Province(17YBA290)

Abstract:

In this paper, the classical risk model is extended to nonhomogeneous compound Poisson risk model. Firstly, both the classical method and the time-varying method are used to calculate the ruin-related quantities for this model, and the analytical expression of the renewal equation is obtained. Secondly, for the time-varying model, the generalized Gerber-Shiu function is defined, which is to verify the effectiveness of the time-varying method for the nonhomogeneous compound Poisson risk model. Finally, when each claim follows an exponentially distribution, the corresponding ruin probability and Gerber-Shiu function are calculated.

Key words: Ruin probability, Time-varying method, Nonhomogeneous Poisson process, Gerber-Shiu function, Renewal equation

CLC Number: 

  • O211.6
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