Mathematics and Financial Economics

, Volume 13, Issue 4, pp 661–719 | Cite as

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

  • Alexis Bismuth
  • Olivier GuéantEmail author
  • Jiang Pu


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 à 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 à 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.


Optimal portfolio choice Optimal execution Optimal portfolio liquidation Optimal portfolio transition Bayesian learning Online learning Stochastic optimal control Hamilton–Jacobi–Bellman equations 


G110 C110 C180 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centre d’Economie de la SorbonneUniversité Paris 1 Panthéon-SorbonneParisFrance
  2. 2.Den-Service de thermo-hydraulique et de mécanique des fluides - Laboratoire de Génie Logiciel pour la Simulation (DEN/STMF/LGLS), CEAUniversité Paris-SaclayGif-sur-YvetteFrance
  3. 3.Institut Europlace de FinanceParisFrance

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