The Wasserstein Metric and Robustness in Risk Management
In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-08-01
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| Series: | Risks |
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| Online Access: | http://www.mdpi.com/2227-9091/4/3/32 |
| _version_ | 1819068751250718720 |
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| author | Rüdiger Kiesel Robin Rühlicke Gerhard Stahl Jinsong Zheng |
| author_facet | Rüdiger Kiesel Robin Rühlicke Gerhard Stahl Jinsong Zheng |
| author_sort | Rüdiger Kiesel |
| collection | DOAJ |
| description | In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other stakeholders have started to require that the internal models used by financial institutions are robust. We present an approach to consistently incorporate the robustness requirements into the quantitative risk management process of a financial institution, with a special focus on insurance. We advocate the Wasserstein metric as the canonical metric for approximations in robust risk management and present supporting arguments. Representing risk measures as statistical functionals, we relate risk measures with the concept of robustness and hence continuity with respect to the Wasserstein metric. This allows us to use results from robust statistics concerning continuity and differentiability of functionals. Finally, we illustrate our approach via practical applications. |
| first_indexed | 2024-12-21T16:39:07Z |
| format | Article |
| id | doaj.art-aeadf0cecf144629a0028292f8ddb97c |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-21T16:39:07Z |
| publishDate | 2016-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-aeadf0cecf144629a0028292f8ddb97c2022-12-21T18:57:09ZengMDPI AGRisks2227-90912016-08-01433210.3390/risks4030032risks4030032The Wasserstein Metric and Robustness in Risk ManagementRüdiger Kiesel0Robin Rühlicke1Gerhard Stahl2Jinsong Zheng3Chair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, Essen 45141, GermanyChair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, Essen 45141, GermanyGroup Risk Management, Talanx AG, Riethorst 2, Hannover 30659, GermanyGroup Risk Management, Talanx AG, Riethorst 2, Hannover 30659, GermanyIn the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other stakeholders have started to require that the internal models used by financial institutions are robust. We present an approach to consistently incorporate the robustness requirements into the quantitative risk management process of a financial institution, with a special focus on insurance. We advocate the Wasserstein metric as the canonical metric for approximations in robust risk management and present supporting arguments. Representing risk measures as statistical functionals, we relate risk measures with the concept of robustness and hence continuity with respect to the Wasserstein metric. This allows us to use results from robust statistics concerning continuity and differentiability of functionals. Finally, we illustrate our approach via practical applications.http://www.mdpi.com/2227-9091/4/3/32risk managementWasserstein metricrobustnessrisk measures |
| spellingShingle | Rüdiger Kiesel Robin Rühlicke Gerhard Stahl Jinsong Zheng The Wasserstein Metric and Robustness in Risk Management Risks risk management Wasserstein metric robustness risk measures |
| title | The Wasserstein Metric and Robustness in Risk Management |
| title_full | The Wasserstein Metric and Robustness in Risk Management |
| title_fullStr | The Wasserstein Metric and Robustness in Risk Management |
| title_full_unstemmed | The Wasserstein Metric and Robustness in Risk Management |
| title_short | The Wasserstein Metric and Robustness in Risk Management |
| title_sort | wasserstein metric and robustness in risk management |
| topic | risk management Wasserstein metric robustness risk measures |
| url | http://www.mdpi.com/2227-9091/4/3/32 |
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