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Multivariate Self-Exciting Processes with Dependencies

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arxiv 2503.15958 v2 pith:R5AFWZA6 submitted 2025-03-20 math.PR q-fin.RM

Caroline Hillairet (CREST) , Thomas Peyrat (CREST) , Anthony Réveillac (INSA Toulouse , IMT , UT) This is my paper · ORCID
classification math.PRq-fin.RM
keywords processesdependenciesclassgeneralriskself-excitingaccountcalculating
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This paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, intensity, and also shifted processes. The framework takes into account dynamic dependencies between the frequency and the severity components of the risk, and therefore induces theoretical challenges in the computations of risk valuations. We present a general method for calculating different quantities related to these MSPDs, which combines the Poisson imbedding, the pseudo-chaotic expansion and Malliavin calculus. The methodology is illustrated for the computation of explicit general correlation formula.

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  1. Functional Laplace Transform of a Multivariate Hawkes Process, Subsequent Characteristics, and Numerical Approximations

    math.PR 2025-07 conditional novelty 6.0 of 10

    A system of Volterra-like integral equations characterizes the multi-temporal Laplace transform and two-time covariance of non-stationary multivariate Hawkes processes.

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