ABSTRACT

In this paper, we study the mean–variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not complete and the drift is uncertain. Then, the optimal strategy based on partial information is derived, which reduces to solving a related backward stochastic differential equation (BSDE). Finally, we propose an efficient numerical scheme to approximate the optimal portfolio that is the solution of the BSDE mentioned above. Malliavin calculus and the particle representation play important roles in this scheme.

中文翻译：

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具有漂移不确定性的部分信息下的均值-方差投资组合选择

摘要

在本文中，我们研究了具有漂移不确定性的部分信息下的均值-方差投资组合选择问题。首先，我们证明即使在这种情况下市场模型也是完整的，而信息不完整且漂移不确定。然后，推导出基于部分信息的最优策略，简化为求解相关的反向随机微分方程（BSDE）。最后，我们提出了一种有效的数值方案来近似最优投资组合，即上述 BSDE 的解决方案。Malliavin 演算和粒子表示在该方案中发挥重要作用。