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Simple bounds for utility maximization with small transaction costs

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  • Bouchard, Bruno
  • Muhle-Karbe, Johannes

Abstract

Using elementary arguments, we show how to 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 pave 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

  • Bouchard, Bruno & Muhle-Karbe, Johannes, 2022. "Simple bounds for utility maximization with small transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 98-113.
    • Handle: RePEc:eee:spapps:v:146:y:2022:i:c:p:98-113
    DOI: 10.1016/j.spa.2022.01.008
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    References listed on IDEAS

    as
    1. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
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