A DUAL CHARACTERIZATION OF SELF-GENERATION AND EXPONENTIAL FORWARD PERFORMANCES

• 成果类型: Article
• 署名作者: Zitkovic, Gordan
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP607
• 发表日期: 2009
• 页码: 2176-2210
• 关键词: unbounded random endowment; incomplete markets; Utility maximization; Optimal investment; martingale measures; optimal consumption; PORTFOLIO POLICIES; constraints

摘要

We propose a mathematical framework for the study of a family of random fields-called forward performances-which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then we focus on random fields with an exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by Ito-processes, where we obtain an explicit parametrization of all exponential forward performances.