IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2011.03314.html
   My bibliography  Save this paper

The importance of dynamic risk constraints for limited liability operators

Author

Listed:
  • John Armstrong
  • Damiano Brigo
  • Alex S. L. Tse

Abstract

Previous literature shows that prevalent risk measures such as Value at Risk or Expected Shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio optimisation. However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the asset performance, the trader's portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market.

Suggested Citation

  • John Armstrong & Damiano Brigo & Alex S. L. Tse, 2020. "The importance of dynamic risk constraints for limited liability operators," Papers 2011.03314, arXiv.org.
    • Handle: RePEc:arx:papers:2011.03314
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2011.03314
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    2. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    3. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    4. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    5. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    6. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Guan, Guohui & Liang, Zongxia, 2016. "Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 224-237.
    9. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    10. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    11. Yiu, K. F. C., 2004. "Optimal portfolios under a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1317-1334, April.
    12. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    13. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
    14. Armstrong, John & Brigo, Damiano, 2019. "Risk managing tail-risk seekers: VaR and expected shortfall vs S-shaped utility," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 122-135.
    15. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    16. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    17. Jennifer Carpenter, 1999. "Does Option Compensation Increase Managerial Risk Appetite?," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-076, New York University, Leonard N. Stern School of Business-.
    18. Maxim Bichuch & Stephan Sturm, 2014. "Portfolio optimization under convex incentive schemes," Finance and Stochastics, Springer, vol. 18(4), pages 873-915, October.
    19. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    20. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    21. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    22. John Armstrong & Damiano Brigo, 2019. "The ineffectiveness of coherent risk measures," Papers 1902.10015, arXiv.org, revised Oct 2020.
    23. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    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. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    2. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    3. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    4. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, June.
    5. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    6. Zongxia Liang & Yang Liu & Litian Zhang, 2021. "A Framework of State-dependent Utility Optimization with General Benchmarks," Papers 2101.06675, arXiv.org, revised Dec 2023.
    7. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    8. Dolf Talman & Zaifu Yang, 2012. "On a Parameterized System of Nonlinear Equations with Economic Applications," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 644-671, August.
    9. Zhiqiang Zheng & Balaji Padmanabhan & Steven O. Kimbrough, 2003. "On the Existence and Significance of Data Preprocessing Biases in Web-Usage Mining," INFORMS Journal on Computing, INFORMS, vol. 15(2), pages 148-170, May.
    10. Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1999. "Variational Inequality Problems With a Continuum of Solutions : Existence and Computation," Other publications TiSEM 73e2f01b-ad4d-4447-95ba-a, Tilburg University, School of Economics and Management.
    11. Carlos R. Handy & Daniel Vrinceanu & Carl B. Marth & Harold A. Brooks, 2015. "Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure," Mathematics, MDPI, vol. 3(4), pages 1-24, November.
    12. Allen C. Goodman & Miron Stano, 2000. "Hmos and Health Externalities: A Local Public Good Perspective," Public Finance Review, , vol. 28(3), pages 247-269, May.
    13. Bode, Sven & Michaelowa, Axel, 2003. "Avoiding perverse effects of baseline and investment additionality determination in the case of renewable energy projects," Energy Policy, Elsevier, vol. 31(6), pages 505-517, May.
    14. Ala, Guido & Fasshauer, Gregory E. & Francomano, Elisa & Ganci, Salvatore & McCourt, Michael J., 2017. "An augmented MFS approach for brain activity reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 3-15.
    15. Bettina Campedelli & Andrea Guerrina & Giulia Romano & Chiara Leardini, 2014. "La performance della rete ospedaliera pubblica della regione Veneto. L?impatto delle variabili ambientali e operative sull?efficienza," MECOSAN, FrancoAngeli Editore, vol. 2014(92), pages 119-142.
    16. Haider A. Khan, 2004. "General Conclusions: From Crisis to a Global Political Economy of Freedom," Palgrave Macmillan Books, in: Global Markets and Financial Crises in Asia, chapter 9, pages 193-211, Palgrave Macmillan.
    17. Penn Loh & Zoë Ackerman & Joceline Fidalgo & Rebecca Tumposky, 2022. "Co-Education/Co-Research Partnership: A Critical Approach to Co-Learning between Dudley Street Neighborhood Initiative and Tufts University," Social Sciences, MDPI, vol. 11(2), pages 1-17, February.
    18. Broekhuis, Manda & Vos, Janita F.J., 2003. "Improving organizational sustainability using a quality perspective," Research Report 03A43, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    19. O'Brien, Raymond & Patacchini, Eleonora, 2003. "Testing the exogeneity assumption in panel data models with "non classical" disturbances," Discussion Paper Series In Economics And Econometrics 0302, Economics Division, School of Social Sciences, University of Southampton.
    20. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2002. "Perfection and Stability of Stationary Points with Applications in Noncooperative Games," Discussion Paper 2002-108, Tilburg University, Center for Economic Research.

    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:2011.03314. 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.