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.

中文翻译：

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漂移不确定性下的投资组合选择，投资组合清算和投资组合转换

本文提出了几种模型，分别针对最优投资组合选择，最优投资组合清算和最优投资组合转移问题，其中风险资产的预期收益是未知的。我们的方法基于贝叶斯学习与动态编程技术之间的耦合，从而导致偏微分方程。它可以在la la Merton框架内恢复Karatzas和Zhao的著名结果，还可以处理mar方法不再可用的情况。尤其是，我们会在àla框架内解决最佳投资组合选择，投资组合清算和投资组合过渡问题 因此，我们建立了一个模型，在该模型中，代理人在决策过程中既考虑资产的流动性，又考虑了预期收益的不确定性。