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On the γ-reflected processes with fBm input*

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Peng Liu

  2. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015, Lausanne, Switzerland

    Enkelejd Hashorva & Lanpeng Ji

Authors
  1. Peng Liu
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  2. Enkelejd Hashorva
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  3. Lanpeng Ji
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Correspondence to Peng Liu.

Additional information

*Supported by the Swiss Nationa l Science Foundation Project 200021-140633/1. P. Liu is also supported by the National Science Foundation of China 11171164.

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Liu, P., Hashorva, E. & Ji, L. On the γ-reflected processes with fBm input*. Lith Math J 55, 402–412 (2015). https://doi.org/10.1007/s10986-015-9288-6

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  • DOI: https://doi.org/10.1007/s10986-015-9288-6

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