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

Author

Listed:
  • Jan Kallsen

    (Munich University of Technology)

  • Johannes Muhle-Karbe

    (Imperial College London - Department of Mathematics)

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.

Suggested Citation

  • Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Swiss Finance Institute Research Paper Series 13-15, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1315
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2246785
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    Citations

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    Cited by:

    1. Filippo Passerini & Samuel E. Vazquez, 2015. "Optimal Trading with Alpha Predictors," Papers 1501.03756, arXiv.org, revised Jan 2015.
    2. Jan Kallsen & Johannes Muhle-Karbe, 2014. "High-Resilience Limits of Block-Shaped Order Books," Papers 1409.7269, arXiv.org.
    3. Kühn, Christoph & Muhle-Karbe, Johannes, 2015. "Optimal liquidity provision," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2493-2515.
    4. M. Abeille & E. Serie & A. Lazaric & X. Brokmann, 2016. "LQG for portfolio optimization," Papers 1611.00997, arXiv.org, revised Nov 2016.
    5. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    6. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
    7. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org, revised Mar 2015.
    8. Richard J Martin, 2016. "Universal trading under proportional transaction costs," Papers 1603.06558, arXiv.org.
    9. Christoph Kuhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision," Papers 1309.5235, arXiv.org, revised Feb 2015.
    10. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    11. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    12. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    13. Dylan Possamai & Guillaume Royer, 2014. "General indifference pricing with small transaction costs," Papers 1401.3261, arXiv.org, revised Apr 2015.

    More about this item

    Keywords

    transaction costs; optimal investment and consumption; trading volume; asymptotics;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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