2016/11/23 by Alexis Bismuth, Bismuth, Alexis, Olivier Guéant +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1611.07843
openalex publication_date 2016/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.