Dual formulation of the utility maximization problem: The case of nonsmooth utility

• 成果类型: Article
• 署名作者: Bouchard, B; Touzi, N; Zeghal, A
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000062
• 发表日期: 2004
• 页码: 678-717
• 关键词: optimal investment

摘要

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization problems in our framework. Second, we allow for the presence of some given liability or a random endowment. In particular, these results provide a dual formulation of the utility indifference valuation rule.