Limit theorems for marked Hawkes processes with application to a risk model. (English) Zbl 1325.60025
Summary: 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 an application in finance.
MSC:
| 60F10 | Large deviations |
| 60F05 | Central limit and other weak theorems |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
large deviation principle; central limit theorem; Hawkes processes; marked point processes; self-exciting processes; risk modelReferences:
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