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

Dmytro Karabash; Lingjiong Zhu

doi:10.1080/15326349.2015.1024868

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

Dmytro Karabash, Lingjiong Zhu

Research output: Contribution to journal › Article › peer-review

30 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 language	English (US)
Pages (from-to)	433-451
Number of pages	19
Journal	Stochastic Models
Volume	31
Issue number	3
DOIs	https://doi.org/10.1080/15326349.2015.1024868
State	Published - Jul 3 2015
Externally published	Yes

Bibliographical note

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

Publisher Copyright:
© 2015 Taylor and Francis Group, LLC.

Keywords

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

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10.1080/15326349.2015.1024868

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title = "Limit Theorems for Marked Hawkes Processes with Application to a Risk Model",

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.",

keywords = "Central limit theorem, Hawkes processes, Large deviations, Marked point processes, Self-exciting processes",

author = "Dmytro Karabash and Lingjiong Zhu",

note = "Funding Information: The authors are both supported by NSF grant DMS-0904701, DARPA grant and MacCracken Fellowship at New York University. Publisher Copyright: {\textcopyright} 2015 Taylor and Francis Group, LLC.",

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AU - Karabash, Dmytro

AU - Zhu, Lingjiong

N1 - Funding Information: The authors are both supported by NSF grant DMS-0904701, DARPA grant and MacCracken Fellowship at New York University. Publisher Copyright: © 2015 Taylor and Francis Group, LLC.

PY - 2015/7/3

Y1 - 2015/7/3

N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Hawkes processes

KW - Large deviations

KW - Marked point processes

KW - Self-exciting processes

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

Abstract

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