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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorRuszel, Wioletta
dc.contributor.authorBergman, Peggy
dc.date.accessioned2023-09-30T23:01:16Z
dc.date.available2023-09-30T23:01:16Z
dc.date.issued2023
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/45291
dc.description.abstractPoint processes in probability theory are special stochastic processes which model the occurrence of events (points) in some space and parameterized by their frequency. Hawkes processes are general point processes where the frequency can be self-exciting or mutually exciting. They occur in various areas such as geological sciences, epidemiology and financial mathematics. The focus of this thesis lies in discussing different types of Hawkes processes and their properties as well as presenting financial applications. The (linear) Hawkes process or self-exciting Hawkes process is a process with a single counting process such that that the occurrence of an event increases the probability of the occurrence of another event. In the case of the (linear) Hawkes process, we prove the Law of Large Numbers and the Central Limit Theorem. Moreover, we study the Hawkes likelihood function and the Hawkes loglikelihood function. Besides a self-exciting Hawkes process there exists a mutually exciting Hawkes process, which is a process with multiple counting processes that are depended on each other. Meaning that the occurrence of an event in one of these counting processes also lead to an increased probability of an event occurring in the other counting processes. We study the Hawkes likelihood function and the Hawkes log-likelihood function for the mutually exciting Hawkes process. The marked Hawkes process is a (linear) Hawkes process with added random variables called the random marks. We prove the Hawkes likelihood function and the Hawkes log-likelihood function as well as the Central Limit Theorem. Furthermore, we derive the dynamics for the Hawkes jump-diffusion model given by three stochastic differential equations and prove the Law of Large Numbers and Central Limit Theorem for this particular model.
dc.description.sponsorshipUtrecht University
dc.language.isoEN
dc.subjectThe focus of this thesis lies in discussing different types of Hawkes processes and their properties as well as presenting financial applications.
dc.titleProperties and Applications of Hawkes Processes
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.courseuuMathematical Sciences
dc.thesis.id19822


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