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Transaction costs and shadow prices in discrete time

Czichowsky, Christoph, Muhle-Karbe, Johannes and Schachermayer, Walter (2013) Transaction costs and shadow prices in discrete time. . The London School of Economics and Political Science, Department of Mathematics, London, UK.

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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.

Item Type: Monograph (Report)
Official URL: http://arxiv.org
Additional Information: © 2013 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
Sets: Departments > Mathematics
Date Deposited: 01 Oct 2013 07:27
Last Modified: 10 Aug 2019 23:12
URI: http://eprints.lse.ac.uk/id/eprint/53250

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