Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

• 成果类型: Article
• 署名作者: Deng, Shuoqing; Tan, Xiaolu; Yu, Xiang
• 署名单位: Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.1029
• 发表日期: 2020
• 页码: 1210-1236
• 关键词: optimal investment; DISCRETE-TIME; fundamental theorem; random endowments; MARKETS; arbitrage; Duality; price

摘要

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numeraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3): 837-860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577-612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577-612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.