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<p>Let <Emphasis Type="BoldItalic">B</Emphasis>(<i>t</i>), <i>t</i> ∈ [0<i>, T</i> ] with <i>T &gt;</i> 0, be a <i>d</i>-dimensional Brownian motion with mutually independent components. Let <Emphasis Type="BoldItalic">η</Emphasis> be a random vector, independent of <Emphasis Type="BoldItalic">B</Emphasis>, with components that are almost surely bounded within fixed finite intervals.</p><p>This paper establishes asymptotic approximations for the simultaneous ruin probability in a multidimensional Brownian risk model with random trend. We study the probability that a <i>d</i>-dimensional Gaussian risk process <Emphasis Type="BoldItalic">X</Emphasis>(<i>t</i>) = <i>AB</i>(<i>t</i>) <i>− ηt</i>, where <i>A</i> is a nondegenerate matrix, simultaneously exceeds prescribed thresholds as the initial capital tends to infinity.</p>

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Multidimensional Brownian risk models with random trend

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Goran Popivoda,
  • Timofei Shashkov

摘要

Let B(t), t ∈ [0, T ] with T > 0, be a d-dimensional Brownian motion with mutually independent components. Let η be a random vector, independent of B, with components that are almost surely bounded within fixed finite intervals.

This paper establishes asymptotic approximations for the simultaneous ruin probability in a multidimensional Brownian risk model with random trend. We study the probability that a d-dimensional Gaussian risk process X(t) = AB(t) − ηt, where A is a nondegenerate matrix, simultaneously exceeds prescribed thresholds as the initial capital tends to infinity.