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Utility maximization with proportional transaction costs under model uncertainty

Deng, Shuoqing; Tan, Xiaolu; Yu, Xiang (2020), Utility maximization with proportional transaction costs under model uncertainty, Mathematics of Operations Research, 45, 4, p. 1193-1620. 10.1287/moor.2019.1029

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Mathematics of Operations Research
Volume
45
Number
4
Publisher
INFORMS - Institute for Operations Research and the Management Sciences
Published in
Paris
Pages
1193-1620
Publication identifier
10.1287/moor.2019.1029
Metadata
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Author(s)
Deng, Shuoqing
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Yu, Xiang
Department of Mechanical Engineering [Hong Kong]
Abstract (EN)
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a semi-static utility maximization for the case of exponential utility preference. The randomization techniques recently developed in [12] allow us to transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space. Using the one-period duality result in [3], together with measurable selection arguments and minimax theorem, we are able to prove all together the existence of the optimal strategy, convex duality theorem as well as the auxiliary dynamic programming principle in our context with transaction costs. As an application of the duality representation, some important features of utility indifference prices are investigated in the robust setting.
Subjects / Keywords
convex duality; randomization method; Utility maximization; transaction costs; model uncertainty; utility indifference pricing

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