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The General Structure of Optimal Investment and Consumption with Small Transaction Costs

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  • Jan Kallsen
  • Johannes Muhle-Karbe

Abstract

We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfare. These reveal the roles of the investors' preferences as well as the market and cost dynamics, and also lead to a fully dynamic model for the implied trading volume. In frictionless models that can be solved in closed form, explicit formulas for the leading-order corrections due to small transaction costs are obtained.

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  • Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    • Handle: RePEc:arx:papers:1303.3148
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    Cited by:

    1. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org, revised Mar 2015.
    2. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    3. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097, arXiv.org, revised Sep 2017.
    4. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    5. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
    6. Filippo Passerini & Samuel E. Vazquez, 2015. "Optimal Trading with Alpha Predictors," Papers 1501.03756, arXiv.org, revised Jan 2015.
    7. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    8. Christoph Kuhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision," Papers 1309.5235, arXiv.org, revised Feb 2015.
    9. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    10. Kim Weston, 2017. "Existence of a Radner equilibrium in a model with transaction costs," Papers 1702.01706, arXiv.org, revised Feb 2018.
    11. Jan Kallsen & Johannes Muhle-Karbe, 2014. "High-Resilience Limits of Block-Shaped Order Books," Papers 1409.7269, arXiv.org.
    12. Dylan Possamai & Guillaume Royer, 2014. "General indifference pricing with small transaction costs," Papers 1401.3261, arXiv.org, revised Apr 2015.
    13. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
    14. Kühn, Christoph & Muhle-Karbe, Johannes, 2015. "Optimal liquidity provision," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2493-2515.
    15. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    16. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.

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