ASYMPTOTICS OF THE PROBABILITY MINIMIZING A DOWN-SIDE RISK

• 成果类型: Article
• 署名作者: Hata, Hiroaki; Nagai, Hideo; Sheu, Shuenn-Jyi
• 署名单位: Academia Sinica - Taiwan; University of Osaka
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP618
• 发表日期: 2010
• 页码: 52-89
• 关键词: sensitive control; Portfolio optimization; utility; management; equation

摘要

We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain explicit solutions for the primal problem.