CONVEX DUALITY FOR STOCHASTIC SINGULAR CONTROL PROBLEMS

• 成果类型: Article
• 署名作者: Bank, Peter; Kauppila, Helena
• 署名单位: Technical University of Berlin; Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1209
• 发表日期: 2017
• 页码: 485-516
• 关键词: OPTIMAL CONSUMPTION; incomplete markets; Optimal investment; continuous-time; intertemporal preferences; Representation theorem; Sufficient conditions; Utility maximization; fundamental theorem; random endowment

摘要

We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer [Ann. Appl Probab. 9 (1999) 904-950] for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the formulation of a suitable duality framework, the identification of the problem's dual functional as well as the full duality for the primal and dual value functions and their optimizers. The scope of our results is illustrated by an irreversible investment problem and the Hindy-Huang-Kreps utility maximization problem for incomplete financial markets.