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<p>In this paper, we derive explicit formulas for approximating dynamic value at risk (VaR) and related risk measures implied from ruin probabilities, by combining Laguerre series expansion and the Dirac delta family method in a novel way. The approximation error is analyzed and convergence rates are obtained. Numerical examples demonstrate the accuracy of the proposed formulas in several common claim size distributions under the compound Poisson risk model.</p>

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Approximating the Dynamic VaR Risk Measure in Ruin Theory

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Zhenyu Cui,
  • Wen Su,
  • Zhimin Zhang

摘要

In this paper, we derive explicit formulas for approximating dynamic value at risk (VaR) and related risk measures implied from ruin probabilities, by combining Laguerre series expansion and the Dirac delta family method in a novel way. The approximation error is analyzed and convergence rates are obtained. Numerical examples demonstrate the accuracy of the proposed formulas in several common claim size distributions under the compound Poisson risk model.