Dassios, Angelos and Zhao, Hongbiao (2011) A dynamic contagion process. Advances in applied probability, 43 (3). pp. 814-846. ISSN 0001-8678
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.
|Additional Information:||© 2011 Advances in Applied Probability|
|Uncontrolled Keywords:||ISI, cluster point process, Cox process with shot noise intensity, dynamic contagion process, Hawkes process, piecewisedeterministic Markov process, self-exciting point process|
|Library of Congress subject classification:||H Social Sciences > HA Statistics|
|Sets:||Departments > Statistics|
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