The time of ultimate recovery in Gaussian risk model

2018/01/08 by Debicki, Krzysztof, Liu, Peng
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1801.02469

Abstract

We analyze the distance R_T(u) between the first and the last passage time of \X(t)-ct:t∈ [0,T]\ at level u in time horizon T∈(0,∞], where X is a centered Gaussian process with stationary increments and c∈ℝ, given that the first passage time occurred before T. Under some tractable assumptions on X, we find Δ(u) and G(x) such that lim_u→∞ℙ(R_T(u)gt;Δ(u)x)=G(x), for x≥ 0. We distinguish two scenarios: T

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