Extremes of vector-valued Gaussian processes with Trend

2018/01/08 by Long Bai, Bai, Long, Krzysztof Dȩbicki +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Probability and Risk Models #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management

paper · pdf · doi:10.48550/arxiv.1801.02465

Abstract

Let X(t)=(X₁(t), …, X_n(t)), t∈ T⊂ ℝ be a centered vector-valued Gaussian process with independent components and continuous trajectories, and h(t)=(h₁(t),…, h_n(t)), t∈ T be a vector-valued continuous function. We investigate the asymptotics of ℙ(sup_{t∈ T} min_{1≤ i≤ n}(X_i(t)+h_i(t))gt;u) as u→∞. As an illustration to the derived results we analyze two important classes of X(t): with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model.

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