This paper presents several models addressing optimal portfolio choice  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 . It permits to recover the well-known results of Karatzas and Zhao in the case of conjugate (Gaussian) priors for the drift distribution  , but also to go beyond the no-friction case, when martingale methods are no longer available. In particular, we address optimal portfolio choice  in a framework \`a la Almgren-Chriss  and we build therefore a model in which the agent takes into account in his /her allocation decision process both the liquidity of assets and the uncertainty with respect to their expected returns. We also address optimal portfolio liquidation and optimal portfolio transition problems .
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 .
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the case of conjugate (Gaussian) priors for the drift distribution
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Merton
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go beyond the no-friction case, when
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/her allocation
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returns. We also address optimal portfolio liquidation and optimal portfolio transition problems
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