Limit Theorems for Marked Hawkes Processes with Application to a Risk Model

Dmytro Karabash, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

This article focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with an example of application in finance.

Original languageEnglish (US)
Pages (from-to)433-451
Number of pages19
JournalStochastic Models
Volume31
Issue number3
DOIs
StatePublished - Jul 3 2015

Bibliographical note

Funding Information:
The authors are both supported by NSF grant DMS-0904701, DARPA grant and MacCracken Fellowship at New York University.

Keywords

  • Central limit theorem
  • Hawkes processes
  • Large deviations
  • Marked point processes
  • Self-exciting processes

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