IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v56y2020i4d10.1007_s10614-019-09954-3.html
   My bibliography  Save this article

Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean

Author

Listed:
  • Argimiro Arratia

    (Barcelona Tech (UPC))

  • Henryk Gzyl

    (IESA)

Abstract

A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset’s price under this measure. But if the market is incomplete, the risk neutral measure is not unique, and there is a range of possible prices for each asset, which can be identified with bid-ask ranges. We present in this paper an effective method to determine the current prices of a collection of assets in incomplete markets, and such that these prices comply with the cost constraints for a portfolio optimization problem. Our workhorse is the method of maximum entropy in the mean to adjust a distortion function from bid-ask market data. This distortion function plays the role of a risk neutral measure, which is used to price the assets, and the distorted probability that it determines reproduces bid-ask market values. We carry out numerical examples to study the effect on portfolio returns of the computation of prices of the assets conforming the portfolio with the proposed methodology.

Suggested Citation

  • Argimiro Arratia & Henryk Gzyl, 2020. "Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 929-952, December.
    • Handle: RePEc:kap:compec:v:56:y:2020:i:4:d:10.1007_s10614-019-09954-3
    DOI: 10.1007/s10614-019-09954-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-019-09954-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-019-09954-3?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. Wu, Xianyi & Wang, Jinglong, 2003. "On Characterization of Distortion Premium Principle," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 1-10, May.
    2. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697, November.
    3. 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.
    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. 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.
    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. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.
    2. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    3. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    4. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    5. Grigorova Miryana, 2014. "Stochastic dominance with respect to a capacity and risk measures," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 259-295, December.
    6. 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.
    7. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    8. Nan Zhang & Heng Xu, 2024. "Fairness of Ratemaking for Catastrophe Insurance: Lessons from Machine Learning," Information Systems Research, INFORMS, vol. 35(2), pages 469-488, June.
    9. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    10. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    11. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    12. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    13. Choo, Weihao & de Jong, Piet, 2009. "Loss reserving using loss aversion functions," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 271-277, October.
    14. 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.
    15. Hernández Solís, Montserrat & Lozano Colomer, Cristina & Vilar Zanón, José Luis, 2013. "La prima de riesgo recargada en un seguro de rentas: tarificación mediante el uso de una medida de riesgo coherente || The Risk Recharged Premium for a Survival Life Insurance: Recharged Premium throu," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 15(1), pages 151-167, June.
    16. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    17. Liu, Fangda & Cai, Jun & Lemieux, Christiane & Wang, Ruodu, 2020. "Convex risk functionals: Representation and applications," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 66-79.
    18. Nendel, Max & Streicher, Jan, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    19. Dilip B. Madan, 2018. "Financial equilibrium with non-linear valuations," Annals of Finance, Springer, vol. 14(2), pages 211-221, May.
    20. Freddy Delbaen, 2021. "Commonotonicity and time-consistency for Lebesgue-continuous monetary utility functions," Finance and Stochastics, Springer, vol. 25(3), pages 597-614, July.

    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:kap:compec:v:56:y:2020:i:4:d:10.1007_s10614-019-09954-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.