Estimation, Sensitivity Analysis, and Optimization of Distortion Risk Measures via Simulation
Abstract
We present a simulation-based method for the estimation, sensitivity analysis, and optimization of distortion risk measures (DRMs), a class of performance measures that capture a wide range of risk attitudes through an underlying distortion function. Existing simulation approaches often approximate DRMs using numerical partitions or empirical distributions. We show that, when the distortion function is piecewise polynomial, the nonlinear structure of a DRM can be handled exactly, without introducing distortion discretization error, using only simulated system outputs. This representation enables the development of a computational method that integrates finite-difference techniques for sensitivity analysis and for solving a broad class of differentiable risk-based optimization problems. Under suitable conditions, we establish strong consistency and convergence rates for DRM estimation, sensitivity analysis, and optimization. We further extend the approach to non-polynomial distortion functions through polynomial approximation. Numerical experiments on synthetic and calibrated financial examples demonstrate the effectiveness and robustness of the proposed approach across a range of applications.
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BibTeX
@misc{cao2026estimation,
title = {{Estimation, Sensitivity Analysis, and Optimization of Distortion Risk Measures via Simulation}},
author = {Hao Cao and Jian-Qiang Hu and Jiaqiao Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13751},
eprint = {2610.13751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13751},
}
RIS
TY - UNPB
TI - Estimation, Sensitivity Analysis, and Optimization of Distortion Risk Measures via Simulation
AU - Hao Cao
AU - Jian-Qiang Hu
AU - Jiaqiao Hu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13751
UR - https://arxiv.org/abs/2610.13751
AB - We present a simulation-based method for the estimation, sensitivity analysis, and optimization of distortion risk measures (DRMs), a class of performance measures that capture a wide range of risk attitudes through an underlying distortion function. Existing simulation approaches often approximate DRMs using numerical partitions or empirical distributions. We show that, when the distortion function is piecewise polynomial, the nonlinear structure of a DRM can be handled exactly, without introducing distortion discretization error, using only simulated system outputs. This representation enables the development of a computational method that integrates finite-difference techniques for sensitivity analysis and for solving a broad class of differentiable risk-based optimization problems. Under suitable conditions, we establish strong consistency and convergence rates for DRM estimation, sensitivity analysis, and optimization. We further extend the approach to non-polynomial distortion functions through polynomial approximation. Numerical experiments on synthetic and calibrated financial examples demonstrate the effectiveness and robustness of the proposed approach across a range of applications.
ER -