Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty

• 成果类型: Article
• 署名作者: Xu, Zuo Quan; Yi, Fahuai
• 署名单位: Hong Kong Polytechnic University; Guangdong University of Foreign Studies
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.0995
• 发表日期: 2020
• 页码: 384-401
• 关键词: optimal stopping problem; valuation; disorder

摘要

In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull or bear) trends of the underlying stock. This is called drift uncertainty. Owing to the unavoidable need for the estimation of trends while making decisions, the related Hamilton-Jacobi-Bellman equation turns out to be of a degenerate parabolic type. Hence, it is very hard to obtain its regularity using the standard approach, making the problem different from the existing optimal redeeming problems without drift uncertainty. We present a thorough and delicate probabilistic and functional analysis to obtain the regularity of the value function and the optimal redeeming strategies. The optimal redeeming strategies of stock loans appear significantly different in the bull and bear trends.