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Number of Claims and Ruin Time for a Refracted Risk Process

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2017 MATRIX Annals

Part of the book series: MATRIX 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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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.

Author information

Authors and Affiliations

  1. Sichuan University, Chengdu, China

    Yanhong Li

  2. Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wrocław, Poland

    Zbigniew Palmowski

  3. Department of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, China

    Chunming Zhao

  4. School of Mathematical Sciences and LPMC Nankai University, Tianjin, China

    Chunsheng Zhang

Authors
  1. Yanhong Li
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  2. Zbigniew Palmowski
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  3. Chunming Zhao
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  4. Chunsheng Zhang
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Corresponding author

Correspondence to Chunming Zhao .

Editor information

Editors and Affiliations

  1. The University of Melbourne, Melbourne, Australia

    Jan de Gier

  2. University of Western Australia, Perth, Australia

    Cheryl E. Praeger

  3. UCLA, Los Angeles, CA, USA

    Terence Tao

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Li, Y., Palmowski, Z., Zhao, C., Zhang, C. (2019). Number of Claims and Ruin Time for a Refracted Risk Process. In: de Gier, J., Praeger, C., Tao, T. (eds) 2017 MATRIX Annals. MATRIX Book Series, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-030-04161-8_49

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