On the gamma-reflected processes with fBm input

2014/02/11 by Peng Liu, Enkelejd Hashorva, Liu, Peng +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1402.2628

arxiv created 2014/02/11 · openalex publication_date 2014/02/11 · arxiv updated 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Define a γ-reflected process W_γ(t)=Y_H(t)-γinf_s∈[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∈ (0,1) and a negative linear trend. In risk theory R_γ(t)=u-W_γ(t), t≥0 is referred to as the risk process with tax of a loss-carry-forward type, whereas in queueing theory W₁ is referred to as the queue length process. In this paper, we investigate the ruin probability and the ruin time of the risk process R_γ, γ∈ [0,1] over a surplus dependent time interval [0, T_u].

Citations

• Conditional limit theorems for regulated fractional Brownian motion
• A note on upper estimates for Pickands constants

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