Transaction Costs, Shadow Prices, and Duality in Discrete Time
AbstractFor 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1205.4643.
Date of creation: May 2012
Date of revision: Jan 2014
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-29 (All new papers)
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