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Approximating the Dynamic VaR Risk Measure in Ruin Theory

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  • Zhenyu Cui

    (Stevens Institute of Technology, School of Business)

  • Wen Su

    (Shandong University of Finance and Economics, School of Insurance)

  • Zhimin Zhang

    (Chongqing University, College of Mathematics and Statistics)

Abstract

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.

Suggested Citation

  • Zhenyu Cui & Wen Su & Zhimin Zhang, 2025. "Approximating the Dynamic VaR Risk Measure in Ruin Theory," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-26, December.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:4:d:10.1007_s11009-025-10233-y
    DOI: 10.1007/s11009-025-10233-y
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