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Ruin by dynamic contagion claims

Author

Listed:
  • Dassios, Angelos
  • Zhao, Hongbiao

Abstract

In this paper, we consider a risk process with the arrival of claims modelled by a dynamic contagion process, a generalisation of the Cox process and Hawkes process introduced by Dassios and Zhao (2011). We derive results for the infinite horizon model that are generalisations of the Cramér–Lundberg approximation, Lundberg’s fundamental equation, some asymptotics as well as bounds for the probability of ruin. Special attention is given to the case of exponential jumps and a numerical example is provided.

Suggested Citation

  • Dassios, Angelos & Zhao, Hongbiao, 2012. "Ruin by dynamic contagion claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 93-106.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:93-106
    DOI: 10.1016/j.insmatheco.2012.03.006
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    Citations

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    Cited by:

    1. Angelos Dassios & Hongbiao Zhao, 2014. "A Markov Chain Model for Contagion," Risks, MDPI, Open Access Journal, vol. 2(4), pages 1-22, November.
    2. Angelos Dassios & Xin Dong, 2014. "Stationarity of Bivariate Dynamic Contagion Processes," Papers 1405.5842, arXiv.org.
    3. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org.
    4. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    5. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.
    6. repec:eee:dyncon:v:79:y:2017:i:c:p:154-183 is not listed on IDEAS
    7. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    8. Kyungsub Lee & Byoung Ki Seo, 2019. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Papers 1908.05089, arXiv.org.
    9. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500030 is not listed on IDEAS
    10. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    11. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    12. Jang, Jiwook & Dassios, Angelos, 2013. "A bivariate shot noise self-exciting process for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 524-532.
    13. repec:eee:insuma:v:74:y:2017:i:c:p:63-77 is not listed on IDEAS

    More about this item

    Keywords

    Dynamic contagion process; Ruin probability; Generalised Lundberg’s fundamental equation; Cramér–Lundberg approximation; Change of measure; Martingale method;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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