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Number of Claims and Ruin Time for a Refracted Risk Process

  • Yanhong Li
  • Zbigniew Palmowski
  • Chunming ZhaoEmail author
  • Chunsheng Zhang
Chapter
Part of the MATRIX Book Series book series (MXBS, volume 2)

Abstract

In this paper, we consider a classical risk model refracted at given level. We give an explicit expression for the joint density of the ruin time and the cumulative number of claims counted up to ruin time. The proof is based on solving some integro-differential equations and employing the Lagrange’s Expansion Theorem.

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Notes

Acknowledgements

Chunming Zhao is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2682017CX065) and by the FP7 Grant PIRSES-GA-2012-318984. Zbigniew Palmowski is supported by the National Science Centre under the grant 2013/09/B/HS4/01496. Zbigniew Palmowski thanks the organizers of the wonderful program Mathematics of Risk for all work done to make this event happened. In particular, he is grateful to Kostya Borovkov (University of Melbourne) and Kais Hamza (Monash University) for all the help and nice discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yanhong Li
    • 1
  • Zbigniew Palmowski
    • 2
  • Chunming Zhao
    • 3
    Email author
  • Chunsheng Zhang
    • 4
  1. 1.Sichuan UniversityChengduChina
  2. 2.Faculty of Pure and Applied MathematicsWrocław University of Science and TechnologyWrocławPoland
  3. 3.Department of Statistics, School of MathematicsSouthwest Jiaotong UniversityChengduChina
  4. 4.School of Mathematical Sciences and LPMC Nankai UniversityTianjinChina

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