Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns

• 成果类型: Article
• 署名作者: Bouchard, B; Pham, H
• 署名单位: 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
• DOI: 10.1214/105051605000000467
• 发表日期: 2005
• 页码: 2393-2421
• 关键词: fundamental theorem; utility; maximization

摘要

We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and Rasonyi Finance and Stochastics 7 (2003) 403-411] and [Schachermayer Math. Finance 14 (2004) 19-48]. In addition to the usual investment in financial assets, we assume that the agents can invest part of their wealth in industrial projects that yield a nonlinear random return. We study the problem of maximizing the utility of consumption on a finite time period. The main difficulty comes from the nonlinearity of the nonfinancial assets' return. Our main result is to show that existence holds in the utility maximization problem. As an intermediary step, we prove the closedness of the set AT of attainable claims under a robust no-arbitrage property similar to the one introduced in [Schachennayer Math. Finance 14 (2004) 19-48] and further discussed in [Kabanov, Stricker and Rdsonyi Finance and Stochastics 7 (2003) 403-411]. This allows us to provide a dual formulation for A(T).