We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime
when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article
is to establish a diffusion approximation by verifying a functional central limit theorem and to compute the ruin probability in finite-time
horizon. Numerical results will also be given. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the
degree of Doctor of Philosophy. / Fall Semester 2018. / November 12, 2018. / diffusion approximation, Hawkes process, risk model / Includes bibliographical references. / Lingjiong Zhu, Professor Directing Dissertation; Xufeng Niu, University Representative; Arash Fahim,
Committee Member; Sanghyun Lee, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_661127 |
| Contributors | Cheng, Zailei (author), Zhu, Lingjiong (professor directing dissertation), Niu, Xufeng, 1954- (university representative), Fahim, Arash (committee member), Lee, Sanghyun (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (104 pages), computer, application/pdf |
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