Limit theorems for a jump-diffusion model with Hawkes jumps

Youngsoo Seol


We consider a jump-diffusion process with Hawkes jumps which has
been widely applied in insurance, finance, queue theory, statistic,
and many other fields. This model can be compared with the
Poissonian jump-diffusion model familiar to financial economists
since Merton~\cite{Merton}. We study the limit theorems for a
jump-diffusion process with Hawkes jumps. In particular, we obtain a
law of large number, central limit theorems, and large deviations
principle. In addition, we give some examples for random variable
$Y_{1}$ to find quantities of several limit behaviors.


Jump-diffusion, Hawkes process, Self-exciting point processes, Law of large number, Central limit theorems, Large deviations principles

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ISSN: 1331-0623 (Print), 1848-8013 (Online)