arXiv 28 Jun 2020 · Finance — Risk Management · publishedQuantitative Finance (2021) · 2 citations (OpenAlex)
arXiv:2006.15491 · PDF · DOI · OpenAlex · Extracted main text
When estimating the risk of a financial position with empirical data or Monte Carlo simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at-Risk (CVaR), it is important to ensure the robustness of the statistical estimator particularly when the data contain noise. Kratscher et al. [1] propose a new framework to examine the qualitative robustness of estimators for tail-dependent law invariant risk measures on Orlicz spaces, which is a step further from earlier work for studying the robustness of risk measurement procedures by Cont et al. [2]. In this paper, we follow the stream of research to propose a quantitative approach for verifying the statistical robustness of tail-dependent law invariant risk measures. A distinct feature of our approach is that we use the Fortet-Mourier metric to quantify the variation of the true underlying probability measure in the analysis of the discrepancy between the laws of the plug-in estimators of law invariant risk measure based on the true data and perturbed data, which enables us to derive an explicit error bound for the discrepancy when the risk functional is Lipschitz continuous with respect to a class of admissible laws. Moreover, the newly introduced notion of Lipschitz continuity allows us to examine the degree of robustness for tail-dependent risk measures. Finally, we apply our quantitative approach to some well-known risk measures to illustrate our theory.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | V. Krätschmer, A. Schied, and H. Zähle, “Qualitative and infinitesim… (2012) Qualitative and infinitesimal robustness of tail-dependent statistical functionals | 1.000 | 23 | 4 | 100% |
| 2 | R. Cont, R. Deguest, and G. Scandolo, “Robustness and sensitivity an… (2010) Robustness and sensitivity analysis of risk measurement procedures | 1.000 | 13 | 5 | 100% |
| 3 | V. Krätschmer, A. Schied, and H. Zähle, “Comparative and qualitative… (2014) Comparative and qualitative robustness for law-invariant risk measures | 1.000 | 7 | 5 | 100% |
| 4 | H. Zähle et al., “Qualitative robustness of statistical functionals… (2015) Qualitative robustness of statistical functionals under strong mixing | 0.928 | 4 | 4 | 100% |
| 5 | H. Föllmer and A. Schied, “Convex measures of risk and trading const… (2002) Convex measures of risk and trading constraints | 0.811 | 4 | 2 | 100% |
| 6 | A. Ben-Tal and M. Teboulle, “An old-new concept of convex risk measu… (2007) An old-new concept of convex risk measures: The optimized certainty equivalent | 0.693 | 5 | 1 | 100% |
| 7 | A. L. Gibbs and F. E. Su, “On choosing and bounding probability metr… (2002) On choosing and bounding probability metrics | 0.644 | 4 | 1 | 100% |
| 8 | P. J. Huber and E. M. Ronchetti, Robust statistics (2011) Springer, 2011 | 0.644 | 2 | 2 | 100% |
| 9 | H. Zähle, “Rates of almost sure convergence of plug-in estimates for… (2011) Rates of almost sure convergence of plug-in estimates for distortion risk measures | 0.644 | 2 | 2 | 100% |
| 10 | H. Zähle, “Qualitative robustness of von mises statistics based on s… (2014) Qualitative robustness of von mises statistics based on strongly mixing data | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 35 scored citations.