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

Alexis Bismuth, Olivier Guéant and Jiang Pu
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Alexis Bismuth: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, SMTH - Service étude et Modélisation en ThermoHydraulique - CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) - CEA - Commissariat à l'énergie atomique et aux énergies alternatives
Jiang Pu: Institut europlace de finance

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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 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.

Keywords: Optimal portfolio choice; Optimal execution; Optimal portfolio liquidation; Optimal portfolio transition; Bayesian learning; Online learning; Stochastic optimal control; Hamilton–Jacobi–Bellman equations (search for similar items in EconPapers)
Date: 2019-09
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Citations: View citations in EconPapers (7)

Published in Mathematics and Financial Economics, 2019, 13 (4), pp.661-719. ⟨10.1007/s11579-019-00241-1⟩

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Working Paper: Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03252482

DOI: 10.1007/s11579-019-00241-1

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