Utility maximization with proportional transaction costs under model uncertainty

Shuoqing Deng, Xiaolu Tan, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-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.

Original languageEnglish
Pages (from-to)1210-1236
Number of pages27
JournalMathematics of Operations Research
Volume45
Issue number4
DOIs
Publication statusPublished - Nov 2020

Keywords

  • Convex duality
  • Model uncertainty
  • Randomization method
  • Transaction costs
  • Utility indifference pricing
  • Utility maximization

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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