Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps

In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point...

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Bibliographic Details
Published in:Journal of applied probability 2014-09, Vol.51 (3), p.699-712
Main Author: Zhu, Lingjiong
Format: Article
Language:English
Subjects:
60F05
60F10
60G07
60G55
Central limit theorem
Cox-Ingersoll-Ross process
Credit risk
Deviation
Excitation
Finance
Hawkes process
Laplace transformation
Laplace transforms
large deviations
Law
Law of large numbers
Martingales
Mathematical models
Mathematical moments
Mathematical theorems
point process
self-exciting process
Stochastic models
Stochastic processes
Studies
Theorems
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Summary:In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1409932668