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September 2014 Approximation of passage times of γ-reflected processes with FBM input
Enkelejd Hashorva, Lanpeng Ji
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J. Appl. Probab. 51(3): 713-726 (September 2014). DOI: 10.1239/jap/1409932669

Abstract

Define a γ-reflected processWγ(t) = YH(t) -γinfs∈[0,t]YH(s),t ≥ 0, with input process{YH(t), t ≥ 0}, which is afractional Brownian motion with Hurst index H ∈ (0, 1) and anegative linear trend. In risk theoryRγ(u) = u - Wγ(t),t ≥ 0, is referred to as the risk process with tax payments of aloss-carry-forward type. For various risk processes, numerous results are knownfor the approximation of the first and last passage times to 0 (ruin times)when the initial reserve u goes to ∞. In this paper we show that,for the γ-reflected process, the conditional (standardized) first andlast passage times are jointly asymptotically Gaussian and completelydependent. An important contribution of this paper is that it links ruinproblems with extremes of nonhomogeneous Gaussian random fields defined byYH, which we also investigate.

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Enkelejd Hashorva. Lanpeng Ji. "Approximation of passage times of γ-reflected processes with FBM input." J. Appl. Probab. 51 (3) 713 - 726, September 2014. https://doi.org/10.1239/jap/1409932669

Information

Published: September 2014
First available in Project Euclid: 5 September 2014

zbMATH: 1303.60027
MathSciNet: MR3256222
Digital Object Identifier: 10.1239/jap/1409932669

Subjects:
Primary: 60G15
Secondary: 60G70

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 3 • September 2014
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