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Stationarity of Bivariate Dynamic Contagion Processes

Author

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  • Angelos Dassios
  • Xin Dong
Abstract
The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors modelled by a shot-noise Cox process and a generalized Hawkes process respectively. In this paper we mainly address the stationarity issue for the BDCP, which is important in applications. We investigate the stationary distribution by applying the the Markov theory on the branching system approximation representation of the BDCP. We find the condition under which there exists a unique stationary distribution of the BDCP intensity and the resulting BDCP has stationary increments. Moments of the stationary intensity are provided by using the Markov property.

Suggested Citation

  • Angelos Dassios & Xin Dong, 2014. "Stationarity of Bivariate Dynamic Contagion Processes," Papers 1405.5842, arXiv.org.
    • Handle: RePEc:arx:papers:1405.5842
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    References listed on IDEAS

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    5. Dassios, Angelos & Zhao, Hongbiao, 2012. "Ruin by dynamic contagion claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 93-106.
    6. 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.
    7. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
    8. Timo Altmann & Thorsten Schmidt & Winfried Stute, 2008. "A Shot Noise Model For Financial Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 87-106.
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    Cited by:

    1. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.

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