On the smoothness of value functions and the existence of optimal strategies in diffusion models

• 成果类型: Article
• 署名作者: Strulovici, Bruno; Szydlowski, Martin
• 署名单位: Northwestern University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2015.03.015
• 发表日期: 2015
• 页码: 1016-1055
• 关键词: Optimal control; optimal stopping; smooth pasting; Super contact; Markov control; HJB equation

摘要

Studies of dynamic economic models often rely on each agent having a smooth value function and a well-defined optimal strategy. For time-homogeneous optimal control problems with a one-dimensional diffusion, we prove that the corresponding value function must be twice continuously differentiable under Lipschitz, growth, and non-vanishing-volatility conditions. Under similar conditions, the value function of any optimal stopping problem is shown to be (once) continuously differentiable. We also provide sufficient conditions, based on comparative statics and differential methods, for the existence of an optimal control in the sense of strong solutions. The results are applied to growth, experimentation, and dynamic contracting settings. (C) 2015 Elsevier Inc. All rights reserved.