2012/05/21 by Christoph Czichowsky, Czichowsky, Christoph, Johannes Muhle‐Karbe +3 · 2 citations
Economics, Econometrics and Finance · #60G48 #91G19 #93E20 #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1205.4643
openalex publication_date 2012/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.