Liu, P, Hashorva, E and Ji, L orcid.org/0000-0002-7790-7765 (2015) On the γ-reflected processes with fBm input. Lithuanian Mathematical Journal, 55 (3). pp. 402-412. ISSN 1573-8825
Abstract
Define a γ-reflected process W γ(t) = Y H (t) − γ inf s ∈ [0. t] Y H (s), t ≽ 0, γ ∈ [0, 1], with {Y H (t), t ≽ 0} a fractional Brownian motion with Hurst index H ∈ (0, 1)and negative linear trend. In risk theory, R γ (t)=u-Wγ(t), t ≽ 0, is the risk process with tax of a loss-carry-forward type and initial reserve u ≽ 0 whereas in queueing theory, W 1 is referred to as the queue length process. In this paper, we investigate the ruin probability and the ruin time of R γ over a reserve-dependent time interval.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Springer Science+Business Media New York.This is a post-peer-review, pre-copyedit version of an article published in Lithuanian Mathematical Journal. The final authenticated version is available online at: http://dx.doi.org/https://10.1007/s10986-015-9288-6 |
Keywords: | γ-reflected process; risk process with tax; ruin probability; ruin time; maximum losses; fractional Brownian motion; Pickands constant; Piterbarg constant |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Jun 2019 11:07 |
Last Modified: | 29 Jun 2019 11:43 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s10986-015-9288-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147170 |