SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 411-436, January 2020.
In this paper, we study a class of optimal investment problems with a nonsmooth and nonconcave utility function, where the value function is the expected utility determined by the state process and time. We adopt partial differential equation methods to prove that the value function belongs to $C^{2,1}$ under some proper conditions of the utility function. Moreover, we analyze the continuity of the optimal strategy and obtain some of its properties around the boundary and the terminal time. Also, an example sheds light on the theoretical results established.

中文翻译：

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有限时间范围内具有非光滑非凹效用的最优投资问题

SIAM金融数学杂志，第11卷，第2期，第411-436页，2020
年1月。在本文中，我们研究了一类具有非光滑和非凹效用函数的最优投资问题，其中价值函数是由状态过程和时间。我们采用偏微分方程方法，证明在效用函数的某些适当条件下，值函数属于$ C ^ {2,1} $。此外，我们分析了最优策略的连续性，并获得了其在边界和终止时间附近的一些属性。同样，通过一个例子可以阐明所建立的理论结果。