Advances in Applied Probability

A dynamic contagion process

Angelos Dassios and Hongbiao Zhao

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We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and exogenous factors of the underlying system. We have systematically analysed the theoretical distributional properties of this new process, based on the piecewise-deterministic Markov process theory developed in Davis (1984), and the extension of the martingale methodology used in Dassios and Jang (2003). The analytic expressions of the Laplace transform of the intensity process and the probability generating function of the point process have been derived. An explicit example of specified jumps with exponential distributions is also given. The object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance, and insurance. We provide an application of this process to credit risk, and a simulation algorithm for further industrial implementation and statistical analysis.

Article information

Adv. in Appl. Probab. Volume 43, Number 3 (2011), 814-846.

First available: 23 September 2011

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Zentralblatt MATH identifier

Mathematical Reviews number (MathSciNet)

Primary: 60J75: Jump processes
Secondary: 60G55: Point processes 60G44: Martingales with continuous parameter 91G40: Credit risk

Dynamic contagion process Cox process with shot noise intensity piecewise-deterministic Markov process cluster point process self-exciting point process Hawkes process


Dassios, Angelos; Zhao, Hongbiao. A dynamic contagion process. Advances in Applied Probability 43 (2011), no. 3, 814--846. doi:10.1239/aap/1316792671.

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