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Bibliographic Details
Main Authors: Hillairet, Caroline, Peyrat, Thomas, Réveillac, Anthony
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.15958
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author Hillairet, Caroline
Peyrat, Thomas
Réveillac, Anthony
author_facet Hillairet, Caroline
Peyrat, Thomas
Réveillac, Anthony
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_15958
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Multivariate Self-Exciting Processes with Dependencies
Hillairet, Caroline
Peyrat, Thomas
Réveillac, Anthony
Probability
Risk Management
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.
title Multivariate Self-Exciting Processes with Dependencies
topic Probability
Risk Management
url https://arxiv.org/abs/2503.15958