DOWNSIDE RISK MINIMIZATION VIA A LARGE DEVIATIONS APPROACH

• 成果类型: Article
• 署名作者: Nagai, Hideo
• 署名单位: University of Osaka
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP781
• 发表日期: 2012
• 页码: 608-669
• 关键词: sensitive control; Portfolio optimization; Bellman equations; management; utility; probability

摘要

We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model, and then study the asymptotic behavior of minimizing probability as T -> infinity. This problem can be closely related to an ergodic risk-sensitive stochastic control problem in the risk-averse case. Indeed, in our main theorem, we relate the former problem concerning the asymptotics for risk minimization to the latter as its dual. As a result, we obtain an expression of the limit value of the probability as the Legendre transform of the value of the control problem, which is characterized as the solution to an H-J-B equation of ergodic type, in the case of a Markovian incomplete market model.