Diffusion Approximation of a Risk Model

• Other Authors: Cheng, Zailei (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Applied mathematics
• Online Access: http://purl.flvc.org/fsu/fd/2018_Fall_Cheng_fsu_0071E_14916

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.