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Transaction Costs and Shadow Prices in Discrete Time

Author

Listed:
  • Christoph Czichowsky

    (Vienna University of Technology)

  • Johannes Muhle-Karbe

    (University of Michigan at Ann Arbor)

  • Walter Schachermayer

    (Universität Wien, Fakultät für Mathematik)

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.

Suggested Citation

  • Christoph Czichowsky & Johannes Muhle-Karbe & Walter Schachermayer, 2013. "Transaction Costs and Shadow Prices in Discrete Time," Swiss Finance Institute Research Paper Series 13-51, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1351
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    File URL: http://ssrn.com/abstract=2342201
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    Cited by:

    1. Ovidiu – Vasile GULER & Corina BOLOȘ, 2021. "Monetization Of Environmental Externalities For Economic Analysis. Case Study: Urban Mobility In Oradea," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 30(2), pages 188-197, December.

    More about this item

    Keywords

    transaction costs; utility maximization; shadow price; convex duality;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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