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A Markov Chain Model for Contagion

Author

Listed:
  • Angelos Dassios

    () (Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • Hongbiao Zhao

    () (Department of Finance, School of Economics & Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China)

Abstract

We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011).

Suggested Citation

  • Angelos Dassios & Hongbiao Zhao, 2014. "A Markov Chain Model for Contagion," Risks, MDPI, Open Access Journal, vol. 2(4), pages 1-22, November.
  • Handle: RePEc:gam:jrisks:v:2:y:2014:i:4:p:434-455:d:42003
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    References listed on IDEAS

    as
    1. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    2. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    3. Dassios, Angelos & Zhao, Hongbiao, 2012. "Ruin by dynamic contagion claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 93-106.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    risk model; contagion risk; bivariate point process; Markov chain model; discretised dynamic contagion process; dynamic contagion process;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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