Transaction Costs and Shadow Prices in Discrete Time

Christoph Czichowsky, Johannes Muhle-Karbe and Walter Schachermayer
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Christoph Czichowsky: Vienna University of Technology
Johannes Muhle-Karbe: University of Michigan at Ann Arbor
Walter Schachermayer: Universität Wien, Fakultät für Mathematik

No 13-51, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even in seemingly perfectly benign situations, i.e., for a log-investor trading in an arbitrage-free market with bounded prices and arbitrarily small transaction costs. We also clarify the connection between shadow prices and duality theory. Whereas dual minimizers need not lead to shadow prices in the above "global" sense, we show that they always correspond to a "local" version.

Keywords: transaction costs; utility maximization; shadow price; convex duality (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2013-10
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1351

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