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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
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    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 obtain.

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    File URL: http://arxiv.org/pdf/1303.3148
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1303.3148.

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    Date of creation: Mar 2013
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    Handle: RePEc:arx:papers:1303.3148

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    Citations

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    Cited by:
    1. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    2. Christoph K\"uhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision in Limit Order Markets," Papers 1309.5235, arXiv.org, revised May 2014.
    3. Ren Liu & Johannes Muhle-Karbe & Marko Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org.
    4. Dylan Possama\"i & Guillaume Royer, 2014. "General indifference pricing with small transaction costs," Papers 1401.3261, arXiv.org.
    5. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org.
    6. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.

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