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http://hdl.handle.net/10397/89349
| 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: http://dx.doi.org/10.1007/s11579-018-0227-2 |
| Appears in Collections: | Journal/Magazine Article |
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| a0601-n05_MFE-2019.pdf | Pre-Published version | 563.37 kB | Adobe PDF | View/Open |
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