Original scientific paper

Limit theorems for a jump-diffusion model with Hawkes jumps

Youngsoo Seol ; Department of Mathematics, Dong-A University, Busan, Saha-gu, Nakdong-daero 550, 37, Republic of Korea

Abstract

We consider a jump-diffusion process with Hawkes jumps, which has been
widely applied in insurance, finance, queueing theory, statistics, and many other fields.
This model can be compared with the Poissonian jump-diffusion model familiar to financial economists since Merton [24]. We study the limit theorems for a jump-diffusion process
with Hawkes jumps. In particular, we obtain the law of large numbers, central limit theorems, and the large deviations principle. In addition, we provide some examples with
i.i.d. random variable Yi that represent the jumps to illustrate the quantities of the limit
behaviors.

Keywords

jump-diffusion, the Hawkes process, self-exciting point processes, the law of large numbers, the central limit theorems, the large deviations principles

Hrčak ID:

252600

URI

https://hrcak.srce.hr/252600

Publication date:

10.3.2021.

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