Approximation of passage times of gamma-reflected processes with fBm input
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State: Public
Version: author
Serval ID
serval:BIB_3A375409985A
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Approximation of passage times of gamma-reflected processes with fBm input
Journal
Journal of Applied Probability
ISSN
0021-9002
Publication state
Published
Issued date
09/2014
Peer-reviewed
Oui
Volume
51
Number
3
Pages
713-726
Language
english
Abstract
Define a gamma-reflected process W-gamma(t) = Y-H(t) - gamma inf(s is an element of[0,t]) Y-H(s), t >= 0, with input process {Y-H(t), t >= 0}, which is a fractional Brownian motion with Hurst index H is an element of (0, 1) and a negative linear trend. In risk theory R-gamma(u) = u - W-gamma(t), t >= 0, is referred to as the risk process with tax payments of a loss-carry-forward type. For various risk processes, numerous results are known for the approximation of the first and last passage times to 0 (ruin times) when the initial reserve u goes to infinity. In this paper we show that, for the gamma-reflected process, the conditional (standardized) first and last passage times are jointly asymptotically Gaussian and completely dependent. An important contribution of this paper is that it links ruin problems with extremes of nonhomogeneous Gaussian random fields defined by Y-H, which we also investigate.
Keywords
Gaussian approximation, passage time, gamma-reflected process, workload process, risk process with tax, fractional Brownian motion, Piterbarg constant, Pickands constant
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Create date
22/10/2013 9:31
Last modification date
21/08/2019 7:08