Uniform asymptotics for the finite-time ruin probability of a generalized bidimensional risk model with Brownian perturbations. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Cheng, Dongya
• Is Part Of: Stochastics. Volume 93:Issue 1(2021)
• Page Start: 56
• Page End: 71
• Publication Date: 2021-01-02
• Subjects: Bidimensional risk model -- finite-time ruin probability -- heavy-tailed claims -- uniform asymptotics -- tail asymptotic independence; Primary: 62P05 -- Secondary: 62E10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1708362
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : This paper considers a generalized bidimensional continuous-time risk model with heavy-tailed claims and Brownian perturbations. In this model, the claim sizes from different lines of business are tail asymptotically independent, while the claim-number processes from different lines of business are arbitrarily dependent. Under some moment conditions on the claim-number processes, an asymptotic formula is established for the finite-time ruin probability defined as the probability that the aggregate surplus process goes below zero over the time horizon [ 0, t ] . The asymptotics holds uniformly for t in some kind of interval. The moment conditions on the claim-number processes are automatically satisfied when the claim-number processes are renewal counting processes. The obtained results confirm that the Brownian perturbations have no influence on the asymptotics of the ruin probability under consideration.