Zhao, Hongbiao
(2012) A Dynamic Contagion Process for Modeling Contagion Risk in Finance and
Insurance. PhD Thesis, LSE-UK.
We introduce a new point process, the dynamic
contagion process, by generalizing the Hawkes process and Cox process with shot
noise intensity. Our process includes both self-excited and externally excited
jumps, which could be used to model the dynamics of contagion impact from
endogenous and exogenous factors of the underlying system. We systematically
analyze 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 Embrechts
(1989). The analytic expressions of the Laplace transform of the intensity
process and probability generating function of the point process are derived. A
simulation algorithm is provided for further industrial implementation and
statistical analysis. Some extensions of this process and comparison with other
similar processes are also investigated. The major object of this study is to
produce a general mathematical framework for modeling 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
apply our research to the default probability of credit risk and ruin
probability of risk theory.
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