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Title: Utility maximization with proportional transaction costs under model uncertainty
Authors: Deng, S
Tan, X
Yu, X 
Issue Date: Nov-2020
Source: Mathematics of operations research, Nov. 2020, v. 45, no. 4, p. 1210-1236
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.
Keywords: Convex duality
Model uncertainty
Randomization method
Transaction costs
Utility indifference pricing
Utility maximization
Publisher: Institute for Operations Research and the Management Sciences
Journal: Mathematics of operations research 
ISSN: 0364-765X
EISSN: 1526-5471
DOI: 10.1287/MOOR.2019.1029
Rights: Copyright: © 2020 INFORMS
This is an Author Accepted Manuscript of an article published by INFORMS, available online: https://doi.org/10.1287/moor.2019.1029
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