Dual formulation of the utility maximization problem under transaction costs

• 成果类型: Article
• 署名作者: Deelstra, G; Pham, H; Touzi, N
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 1353-1383
• 关键词: consumption; portfolio

摘要

In the context of a general multivariate financial market with transaction costs, we consider the problem of maximizing expected utility from terminal wealth. In contrast with the existing literature, where only the liquidation value of the terminal portfolio is relevant, we consider general utility functions which are only required to be consistent with the structure of the transaction costs. An important feature of our analysis is that the utility function is not required to be C-1. Such nonsmoothness is suggested by major natural examples. Our main result is an extension of the well-known dual formulation of the utility maximization problem to this context.