标题： 光滑值函数对于一类非光滑效用最大化问题 显示英文标题

标题： Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

摘要： 在本文中，我们证明了对于一大类带有约束的问题，其效用函数不一定可微或严格凹，HJB方程存在光滑的经典解。如果允许的控制满足可积性条件，或者在其定义域的闭包上连续，则值函数是光滑的。关键思想是研究对偶控制问题和对偶HJB方程。我们构造了一个光滑且严格凸的对偶HJB方程的解，并证明其共轭函数是满足终端和边界条件的原始HJB方程的光滑且严格凹的解。 显示英文摘要

摘要： In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.