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Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims

Zailei Cheng (zcheng@math.fsu.edu) and Youngsoo Seol (prosul76@dau.ac.kr)
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Zailei Cheng: Florida State University
Youngsoo Seol: Dong-A University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 2, 555-571

Abstract: Abstract 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.

Keywords: Diffusion approximation; Risk process; Finite-horizon ruin probability; Hawkes processes; Primary 91B30; Secondary 60F17; 60G55 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11009-019-09722-8

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