IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1611.07843.html
   My bibliography  Save this paper

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Author

Listed:
  • Alexis Bismuth
  • Olivier Gu'eant
  • Jiang Pu

Abstract

This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It enables to recover the well-known results of Karatzas and Zhao in a framework \`a la Merton, but also to deal with cases where martingale methods are no longer available. In particular, we address optimal portfolio choice, portfolio liquidation, and portfolio transition problems in a framework \`a la Almgren-Chriss, and we build therefore a model in which the agent takes into account in his decision process both the liquidity of assets and the uncertainty with respect to their expected return.

Suggested Citation

  • Alexis Bismuth & Olivier Gu'eant & Jiang Pu, 2016. "Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty," Papers 1611.07843, arXiv.org, revised Mar 2019.
  • Handle: RePEc:arx:papers:1611.07843
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1611.07843
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Olivier Guéant & Jiang Pu & Guillaume Royer, 2015. "Accelerated Share Repurchase: Pricing And Execution Strategy," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    2. 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.
    3. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    4. Olivier Guéant, 2015. "Optimal Execution and Block Trade Pricing: A General Framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 336-365, September.
    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    6. 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.
    7. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    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. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    2. Shubhangi Sikaria & Rituparna Sen & Neelesh S. Upadhye, 2019. "Bayesian Filtering for Multi-period Mean-Variance Portfolio Selection," Papers 1911.07526, arXiv.org, revised Aug 2020.
    3. Horst, Ulrich & Xia, Xiaonyu & Zhou, Chao, 2021. "Portfolio Liquidation under Factor Uncertainty," Rationality and Competition Discussion Paper Series 274, CRC TRR 190 Rationality and Competition.
    4. Dammann, Felix & Ferrari, Giorgio, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Center for Mathematical Economics Working Papers 663, Center for Mathematical Economics, Bielefeld University.
    5. Felix Dammann & Giorgio Ferrari, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Papers 2202.10414, arXiv.org, revised Nov 2022.
    6. Fayc{c}al Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Papers 2202.07478, arXiv.org, revised Aug 2023.
    7. Dongmei Zhu & Harry Zheng, 2022. "Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 191-219, July.
    8. Qixuan Luo & Shijia Song & Handong Li, 2023. "Research on the Effects of Liquidation Strategies in the Multi-asset Artificial Market," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1721-1750, December.
    9. Carmine De Franco & Johann Nicolle & Huy^en Pham, 2020. "Discrete-time portfolio optimization under maximum drawdown constraint with partial information and deep learning resolution," Papers 2010.15779, arXiv.org, revised Oct 2020.
    10. Andrea Mazzon & Peter Tankov, 2024. "Optimal stopping and divestment timing under scenario ambiguity and learning," Papers 2408.09349, arXiv.org, revised Oct 2024.
    11. Philippe Bergault & Fayc{c}al Drissi & Olivier Gu'eant, 2021. "Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics," Papers 2103.13773, arXiv.org, revised Mar 2022.
    12. Ulrich Horst & Xiaonyu Xia & Chao Zhou, 2019. "Portfolio liquidation under factor uncertainty," Papers 1909.00748, arXiv.org.

    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. Börsch-Supan, Axel & Ludwig, Alexander & Sommer, Mathias, 2005. "Aging and asset prices," Papers 07-29, Sonderforschungsbreich 504.
    2. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    3. Merton, Robert C., 1993. "On the microeconomic theory of investment under uncertainty," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 13, pages 601-669, Elsevier.
    4. Kaminski, Kathryn M. & Lo, Andrew W., 2014. "When do stop-loss rules stop losses?," Journal of Financial Markets, Elsevier, vol. 18(C), pages 234-254.
    5. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    6. Carlos Eduardo Meyer dos Santos & Marcos Antonio C. da Silveira, 2010. "Depósitos Em Moeda Estrangeira Como Hedge Para Investidores Brasileiros De Longo Prazo: Uma Aplicação Da Teoria Da Escolha Estratégica De Portfólio," Discussion Papers 1462, Instituto de Pesquisa Econômica Aplicada - IPEA.
    7. David Schröder, 2013. "Asset allocation in private wealth management: Theory versus practice," Journal of Asset Management, Palgrave Macmillan, vol. 14(3), pages 162-181, June.
    8. Alan J. Auerbach, 1981. "Evaluating the Taxation of Risky Assets," NBER Working Papers 0806, National Bureau of Economic Research, Inc.
    9. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    10. John H. Cochrane, 1999. "New facts in finance," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 23(Q III), pages 36-58.
    11. Letendre, Marc-Andre & Smith, Gregor W., 2001. "Precautionary saving and portfolio allocation: DP by GMM," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 197-215, August.
    12. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    13. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    14. Annette Vissing-Jorgensen, 2000. "Towards an Explanation of Household Portfolio Choice Heterogeneity: Nonfinancial Income and Participation Cost Structures," Econometric Society World Congress 2000 Contributed Papers 1102, Econometric Society.
    15. Constantino J. Gode, 2001. "Sovereign Debt and Uncertainty in the Mozambican Economy," WIDER Working Paper Series DP2001-130, World Institute for Development Economic Research (UNU-WIDER).
    16. Luc Arrondel & André Masson, 1989. "Déterminants individuels de la composition du patrimoine : France 1980," Revue Économique, Programme National Persée, vol. 40(3), pages 441-502.
    17. Penikas, Henry, 2010. "Copula-Models in Foreign Exchange Risk-Management of a Bank," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 17(1), pages 62-87.
    18. Mark E. Wohar & David E. Rapach, 2005. "Return Predictability and the Implied Intertemporal Hedging Demands for Stocks and Bonds: International Evidence," Computing in Economics and Finance 2005 329, Society for Computational Economics.
    19. Nicolas Aubert & Thomas Rapp, 2008. "Les salariés actionnaires:pourquoi investissent-ils dans leur entreprise?," Revue Finance Contrôle Stratégie, revues.org, vol. 11(4), pages 87-110, December.
    20. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.

    More about this item

    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:1611.07843. 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.