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Simple Bounds for Transaction Costs

Author

Listed:
  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, PSL - Université Paris Sciences et Lettres)

  • Johannes Muhle-Karbe

    (University of Michigan [Ann Arbor] - University of Michigan System)

Abstract

Using elementary arguments, we derive Lp-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which paves the way for its asymptotic analysis using stability results for viscosity solutions. Using tools from Malliavin calculus, we also derive simple sufficient conditions for the regularity of frictionless optimal trading strategies, the second main ingredient for the asymptotic analysis of small transaction costs.

Suggested Citation

  • Bruno Bouchard & Johannes Muhle-Karbe, 2022. "Simple Bounds for Transaction Costs," Post-Print hal-01711371, HAL.
    • Handle: RePEc:hal:journl:hal-01711371
    DOI: 10.1016/j.spa.2022.01.008
    Note: View the original document on HAL open archive server: https://hal.science/hal-01711371
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    References listed on IDEAS

    as
    1. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
    2. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2017. "Trading With Small Price Impact," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 350-400, April.
    3. Jan Kallsen & Johannes Muhle-Karbe, 2017. "The General Structure Of Optimal Investment And Consumption With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 659-703, July.
    4. Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
    5. repec:dau:papers:123456789/6867 is not listed on IDEAS
    6. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    7. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324, July.
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    9. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    10. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    11. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    12. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134, April.
    13. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    14. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    15. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    16. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Transaction costs; Utility maximization; Asymptotic analysis;
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