Approximating the Dynamic VaR Risk Measure in Ruin Theory

Zhenyu Cui (), Wen Su () and Zhimin Zhang ()
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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

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-26

Abstract: 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.

Keywords: Ruin probabilities; Dynamic VaR; Laguerre series expansion; Dirac delta family; Complex-step method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10233-y

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