A unified framework for utility maximization problems: An Orlicz space approach

• 成果类型: Article
• 署名作者: Biagini, Sara; Frittelli, Marco
• 署名单位: University of Milan; University of Perugia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP469
• 发表日期: 2008
• 页码: 929-966
• 关键词: Incomplete markets; Optimal investment; WEALTH

摘要

We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth, with utility functions that are finite-valued over (a,infinity), a is an element of [-infinity, infinity), and satisfy weak regularity assumptions. We adopt a class of trading strategies that allows for stochastic integrals that are not necessarily bounded from below. The embedding of the utility maximization problem in Orlicz spaces permits us to formulate the problem in a unified way for both the cases a is an element of R and a = -infinity. By duality methods, we prove the existence of solutions to the primal and dual problems and show that a singular component in the pricing functionals may also occur with utility functions finite on the entire real line.