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Duality Theory for Portfolio Optimisation under Transaction Costs

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  • Christoph Czichowsky
  • Walter Schachermayer

Abstract

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a predictable and an optional strong supermartingale and pertains to all strategies which remain solvent under transaction costs. We provide examples showing that in the present general setting the shadow price process has to be of this generalised form.

Suggested Citation

  • Christoph Czichowsky & Walter Schachermayer, 2014. "Duality Theory for Portfolio Optimisation under Transaction Costs," Papers 1408.5989, arXiv.org.
    • Handle: RePEc:arx:papers:1408.5989
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    References listed on IDEAS

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    Cited by:

    1. Abdelghani, Mohamed N. & Melnikov, Alexander V., 2017. "On linear stochastic equations of optional semimartingales and their applications," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 207-214.
    2. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2015. "The pricing of contingent claims and optimal positions in asymptotically complete markets," Papers 1509.06210, arXiv.org, revised Sep 2016.
    3. Czichowsky, Christoph & Schachermayer, Walter & Yang, Junjian, 2017. "Shadow prices for continuous processes," LSE Research Online Documents on Economics 63370, London School of Economics and Political Science, LSE Library.
    4. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    5. Christoph Czichowsky & Walter Schachermayer & Junjian Yang, 2014. "Shadow prices for continuous processes," Papers 1408.6065, arXiv.org, revised May 2015.

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