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Utility maximization with proportional transaction costs under model uncertainty

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1805.06498.pdf (445.7Kb)
Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01968750
Dewey
Probabilités et mathématiques appliquées
Sujet
convex duality; randomization method; Utility maximization; transaction costs; model uncertainty; utility indifference pricing
URI
https://basepub.dauphine.fr/handle/123456789/18667
Collections
  • CEREMADE : Publications
Metadata
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Author
Deng, Shuoqing
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Yu, Xiang
51593 Department of Mechanical Engineering [Hong Kong]
Type
Document de travail / Working paper
Item number of pages
27
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.

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