We present a modified verification theorem for the equilibrium control of a general class of portfolio problems. The general class of portfolio problems studied in this paper, is characterized by an objective where the investor seeks to maximize a functional of two conditional expectations of terminal wealth. The objective functional is allowed to be non-linear in the conditional expectations, and thus the problem class is in general terms time-inconsistent. In addition, we provide a corrected proof of the verification theorem and apply the theorem to a number of quadratic, time-inconsistent portfolio problems and determine their solutions. Some of the quadratic portfolio problems have not previously been solved analytically.

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在条件期望之间具有非线性的目标函数的最优控制：一类时间不一致的投资组合问题的解决方案

我们提出了一个修正的验证定理，用于一般类别的投资组合问题的均衡控制。本文研究的一般投资组合问题，其特征是一个目标，即投资者力求最大程度地发挥对终端财富的两个有条件期望的功能。在期望的条件下，目标函数可以是非线性的，因此，问题类别通常是时间不一致的。此外，我们提供了验证定理的校正证明，并将该定理应用于许多二次，时间不一致的投资组合问题，并确定其解决方案。某些二次投资组合问题以前尚未通过分析得到解决。