IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v35y2018i1-2p35-50n3.html
   My bibliography  Save this article

Distortion risk measures, ROC curves, and distortion divergence

Author

Listed:
  • Schumacher Johannes M.

    (Faculty of Economics and Business, Section Quantitative Economics, University of Amsterdam, Roetersstraat 11, Amsterdam, Netherlands)

Abstract

Distortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between distortion functions on the one hand, and ROC curves on the other. This leads to a new interpretation of some well-known classes of distortion risk measures, and to a new notion of divergence between probability measures.

Suggested Citation

  • Schumacher Johannes M., 2018. "Distortion risk measures, ROC curves, and distortion divergence," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 35-50, January.
    • Handle: RePEc:bpj:strimo:v:35:y:2018:i:1-2:p:35-50:n:3
    DOI: 10.1515/strm-2017-0012
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/strm-2017-0012
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/strm-2017-0012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    2. Thomas J. Sargent & Riccardo Colacito & Lars P. Hansen & Timothy Cogley, 2008. "Robustness and US Monetary," 2008 Meeting Papers 228, Society for Economic Dynamics.
    3. Young, Virginia R., 1999. "Optimal insurance under Wang's premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 109-122, November.
    4. Lars Peter Hansen & Thomas J. Sargent, 2008. "Time Inconsistency of Robust Control?," Chapters, in: Roger E.A. Farmer (ed.), Macroeconomics in the Small and the Large, chapter 7, Edward Elgar Publishing.
    5. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Li-Lin Ku & Chien-Pai Han, 2008. "Robust testing procedures of process locations," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(5), pages 579-595, October.
    8. Boonen, Tim J., 2015. "Competitive Equilibria With Distortion Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 703-728, September.
    9. Arnold, Barry C, et al, 1987. "Generating Ordered Families of Lorenz Curves by Strongly Unimodal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 305-308, April.
    10. Lynn Wirch, Julia & Hardy, Mary R., 1999. "A synthesis of risk measures for capital adequacy," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 337-347, December.
    11. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    12. Hans, Erwin & Wullink, Gerhard & van Houdenhoven, Mark & Kazemier, Geert, 2008. "Robust surgery loading," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1038-1050, March.
    13. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    14. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    15. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    16. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    17. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    18. Tsanakas, Andreas, 2004. "Dynamic capital allocation with distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 223-243, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    2. Djeutem, Edouard, 2014. "Model uncertainty and the Forward Premium Puzzle," Journal of International Money and Finance, Elsevier, vol. 46(C), pages 16-40.
    3. Xin Li & Borghan N. Narajabad & Ted Temzelides, 2014. "Robust Dynamic Optimal Taxation and Environmental Externalities," Finance and Economics Discussion Series 2014-75, Board of Governors of the Federal Reserve System (U.S.).
    4. Asano, Takao & Shibata, Akihisa, 2011. "Optimal pricing and quality choice of a monopolist under Knightian uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(6), pages 746-754.
    5. Dennis, Richard, 2014. "Imperfect credibility and robust monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 218-234.
    6. Leitner, Johannes, 2005. "Dilatation monotonous Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 994-1006, December.
    7. Hansen, Lars Peter & Sargent, Thomas J., 2011. "Robustness and ambiguity in continuous time," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1195-1223, May.
    8. Yuan, Hongmin & Jiang, Long & Tian, Dejian, 2020. "Representation theorems for WVaR with respect to a capacity," Statistics & Probability Letters, Elsevier, vol. 158(C).
    9. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    10. Kwon, Hyosung & Miao, Jianjun, 2017. "Three types of robust Ramsey problems in a linear-quadratic framework," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 211-231.
    11. Iverson, Terrence, 2012. "Communicating Trade-offs amid Controversial Science: Decision Support for Climate Policy," Ecological Economics, Elsevier, vol. 77(C), pages 74-90.
    12. Cukierman, Alex & Izhakian, Yehuda, 2015. "Bailout uncertainty in a microfounded general equilibrium model of the financial system," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 160-179.
    13. Dennis, Richard & Kirsanova, Tatiana, 2016. "Computing Markov-Perfect Optimal Policies In Business-Cycle Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(7), pages 1850-1872, October.
    14. Paolo Vitale, 2017. "Ambiguity-aversion in a Single Auction Market," Economics Bulletin, AccessEcon, vol. 37(3), pages 1745-1752.
    15. Dennis, Richard, 2013. "Asset Prices, Business Cycles, and Markov-Perfect Fiscal Policy when Agents are Risk-Sensitive," SIRE Discussion Papers 2013-79, Scottish Institute for Research in Economics (SIRE).
    16. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    17. Sorge, Marco M., 2013. "Robust delegation with uncertain monetary policy preferences," Economic Modelling, Elsevier, vol. 30(C), pages 73-78.
    18. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    19. Gabriela Zeller & Matthias Scherer, 2023. "Risk mitigation services in cyber insurance: optimal contract design and price structure," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 502-547, April.
    20. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:strimo:v:35:y:2018:i:1-2:p:35-50:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.