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Transaction costs, shadow prices, and duality in discrete time

Czichowsky, Christoph, Muhle-Karbe, Johannes and Schachermayer, Walter (2014) Transaction costs, shadow prices, and duality in discrete time. SIAM Journal on Financial Mathematics, 5 (1). pp. 258-277. ISSN 1945-497X

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Identification Number: 10.1137/130925864


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 counterexample, 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 above “global” sense, we show that they always correspond to a “local” version.

Item Type: Article
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Additional Information: © 2014 Society for Industrial and Applied Mathematics
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 01 May 2014 12:20
Last Modified: 16 May 2024 01:50

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