Approximating the Dynamic VaR Risk Measure in Ruin Theory

Zhenyu Cui; Wen Su; Zhimin Zhang

doi:10.1007/s11009-025-10233-y

Approximating the Dynamic VaR Risk Measure in Ruin Theory

Zhenyu Cui
, Wen Su
, Zhimin Zhang

School of Business

Shandong University of Finance and Economics
Chongqing University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	99
Journal	Methodology and Computing in Applied Probability
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s11009-025-10233-y
State	Published - Dec 2025

Keywords

Complex-step method
Dirac delta family
Dynamic VaR
Laguerre series expansion
Ruin probabilities

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10.1007/s11009-025-10233-y

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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.",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

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N2 - 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.

AB - 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.

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KW - Dirac delta family

KW - Dynamic VaR

KW - Laguerre series expansion

KW - Ruin probabilities

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Approximating the Dynamic VaR Risk Measure in Ruin Theory

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Keywords

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