Optimal investment with random endowments in incomplete markets

• 成果类型: Article
• 署名作者: Hugonnier, J; Kramkov, D
• 署名单位: Universite de Montreal; HEC Montreal; Universite de Montreal; Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000134
• 发表日期: 2004
• 页码: 845-864
• 关键词: CONTINGENT CLAIMS; fundamental theorem; optimal consumption; PORTFOLIO POLICIES; arbitrage; constraints; prices

摘要

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random endowments. We show that this approach leads to a dual problem, whose solution is always attained in the space of random variables. In particular, this technique does not require the use of finitely additive measures and the related assumption that the endowments are bounded.