IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1910.14005.html
   My bibliography  Save this paper

Portfolio Optimization with Expectile and Omega Functions

Author

Listed:
  • Alexander Wagner
  • Stan Uryasev

Abstract

This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and general theory about subgradients of risk measures. We also give an elementary derivation of the gradient of negative expectile under some assumptions and provide an example where negative expectile is demonstrably not differentiable. We conducted a case study and solved portfolio optimization problems with negative expectile objective and constraint.

Suggested Citation

  • Alexander Wagner & Stan Uryasev, 2019. "Portfolio Optimization with Expectile and Omega Functions," Papers 1910.14005, arXiv.org.
    • Handle: RePEc:arx:papers:1910.14005
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1910.14005
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    2. Bellini, Fabio & Bignozzi, Valeria & Puccetti, Giovanni, 2018. "Conditional expectiles, time consistency and mixture convexity properties," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 117-123.
    3. Fabio Bellini & Elena Di Bernardino, 2017. "Risk management with expectiles," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 487-506, May.
    4. 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.
    5. Fabio Bellini & Bernhard Klar & Alfred Müller, 2018. "Expectiles, Omega Ratios and Stochastic Ordering," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 855-873, September.
    6. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    7. Fabio Bellini & Ilia Negri & Mariya Pyatkova, 2019. "Backtesting VaR and expectiles with realized scores," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 119-142, March.
    8. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
    2. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.

    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. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.
    2. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    3. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    4. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    5. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    6. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    7. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2021. "ExpectHill estimation, extreme risk and heavy tails," Journal of Econometrics, Elsevier, vol. 221(1), pages 97-117.
    8. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2023. "An expectile computation cookbook," TSE Working Papers 23-1458, Toulouse School of Economics (TSE).
    9. Fabio Bellini & Tolulope Fadina & Ruodu Wang & Yunran Wei, 2020. "Parametric measures of variability induced by risk measures," Papers 2012.05219, arXiv.org, revised Apr 2022.
    10. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    11. Damiano Rossello, 2022. "Performance measurement with expectiles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 343-374, June.
    12. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.
    13. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    14. Di Bernardino, Elena & Laloë, Thomas & Pakzad, Cambyse, 2024. "Estimation of extreme multivariate expectiles with functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    15. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    16. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2024. "Testing Granger non-causality in expectiles," Econometric Reviews, Taylor & Francis Journals, vol. 43(1), pages 30-51, January.
    17. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    18. Qinyu Wu & Fan Yang & Ping Zhang, 2023. "Conditional generalized quantiles based on expected utility model and equivalent characterization of properties," Papers 2301.12420, arXiv.org.
    19. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    20. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1910.14005. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.