Shadow prices for continuous processes

Christoph Czichowsky, Walter Schachermayer and Junjian Yang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: In a financial market with a continuous price process and proportional transaction costs, we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e., a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of "no unbounded profit with bounded risk". A counterexample reveals that these hypotheses cannot be relaxed.

Keywords: utility maximization; proportional transaction costs; convex duality; shadow prices; continuous price processes (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2017-07-01
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Published in Mathematical Finance, 1, July, 2017, 27(3), pp. 623-658. ISSN: 0960-1627

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