与投资问题相关的原始和对偶动态价值函数的正则性
On regularity of primal and dual dynamic value functions related to investment problem
摘要：
研究了效用函数定义在整条实数线上的最优投资原始问题和对偶问题的动态值函数的正则性。建立了原始问题和对偶问题的价值过程分解项之间的关系以及基本问题和条件效用最大化问题的最优解之间的关系。利用这些性质证明了该值函数满足相应的倒向随机偏微分方程。在完全市场的情况下，我们给出了当这个方程有解时效用函数的条件。
英文摘要：
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximization problems are established. These properties are used to show that the value function satisfies a corresponding backward stochastic partial differential equation. In the case of complete markets we give conditions on the utility function when this equation admits a solution.
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