On the tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures

On the tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article On the tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures Zhangting Chen, Dongya Cheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4624067/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Nov, 2024 Read the published version in Methodology and Computing in Applied Probability → Version 1 posted 9 You are reading this latest preprint version Abstract This paper considers the asymptotic behavior for the tail probability of randomly weighted sum Sθ 2 = θ1X1+θ2X2, where X1, X2, θ1, and θ2 are non-negative dependent random variables with distributions F1, F2, G1, and G2, respectively. We obtain the tail-equivalence of P Sθ 2 > x and P(θ1X1 > x)+P(θ2X2 > x) as x → ∞ and some closure properties of distribution classes in three cases: (i). θ1, θ2 are bounded and F1, F2 are subexponential; (ii). θ1, θ2 satisfy the condition of Theorem 2.1 of Tang (2006) [33] and F1, F2 are subexponential with positive lower Matuszewska indices; (iii). θ1, θ2 satisfy the condition of Theorem 3.3 (iii) of Cline and Samorodnitsky (1994) [12] and F1, F2 are long-tailed and dominatedlyvarying- tailed. Furthermore, when F1 and F2 are regularly-varying-tailed, a more transparent result is established and applied to obtain asymptotic results for risk measures. Some numerical studies are conducted to check the accuracy of the obtained results. Randomly weighted sum Dependent random variable Subexponential distribution Risk measure Numerical study Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Nov, 2024 Read the published version in Methodology and Computing in Applied Probability → Version 1 posted Editorial decision: Revision requested 16 Sep, 2024 Reviews received at journal 14 Sep, 2024 Reviews received at journal 28 Aug, 2024 Reviewers agreed at journal 14 Jul, 2024 Reviewers agreed at journal 12 Jul, 2024 Reviewers invited by journal 12 Jul, 2024 Editor assigned by journal 04 Jul, 2024 Submission checks completed at journal 26 Jun, 2024 First submitted to journal 23 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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