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On the existence of shadow prices

Giuseppe Benedetti (), Luciano Campi (), Jan Kallsen () and Johannes Muhle-Karbe ()

Finance and Stochastics, 2013, vol. 17, issue 4, 818 pages

Abstract: For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless shadow market that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper, we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid–ask spreads. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Transaction costs; Shadow prices; Short selling constraints; 91G10; 91B16; G11 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00780-012-0201-4

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