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Title: Optimal investment with random endowments and transaction costs : duality theory and shadow prices
Authors: Bayraktar, E
Yu, X 
Issue Date: Mar-2019
Source: Mathematics and financial economics, Mar. 2019, v. 13, no. 2, p. 253-286
Abstract: This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the duality approach. As an important application of the duality theorem, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form similar to Czichowsky and Schachermayer (Ann Appl Probab 26(3):1888–1941, 2016) as well as in the usual sense using acceptable portfolios.
Keywords: Acceptable portfolios
Convex duality
Proportional transaction costs
Shadow prices
Unbounded random endowments
Utility maximization
Publisher: Springer
Journal: Mathematics and financial economics 
ISSN: 1862-9679
EISSN: 1862-9660
DOI: 10.1007/s11579-018-0227-2
Rights: © Springer-Verlag GmbH Germany, part of Springer Nature 2018
This is a post-peer-review, pre-copyedit version of an article published in Mathematics and Financial Economics. The final authenticated version is available online at:
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