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Asymptotics for Fixed Transaction Costs

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  • Albert Altarovici
  • Johannes Muhle-Karbe
  • H. Mete Soner
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    Abstract

    An investor with constant relative risk aversion trades a safe and several risky assets with constant investment opportunities. For a small fixed transaction cost, levied on each trade regardless of its size, we explicitly determine the leading-order corrections to the frictionless value function and optimal policy.

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    File URL: http://arxiv.org/pdf/1306.2802
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1306.2802.

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    Date of creation: Jun 2013
    Date of revision: Oct 2013
    Handle: RePEc:arx:papers:1306.2802

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    Web page: http://arxiv.org/

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    References

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    1. 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.
    2. Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, 02.
    3. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
    4. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335.
    5. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org.
    6. Anthony W. Lynch & Pierluigi Balduzzi, 1998. "Predictability and Transaction Costs: The Impact on Rebalancing Rules and Behavior," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-049, New York University, Leonard N. Stern School of Business-.
    7. Richard J. Martin, 2012. "Optimal multifactor trading under proportional transaction costs," Papers 1204.6488, arXiv.org.
    8. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    9. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
    10. C. Atkinson & P. Wilmott, 1995. "Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 357-367.
    11. 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, 05.
    12. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
    13. 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.
    14. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
    15. Anthony W. Lynch & Sinan Tan, 2011. "Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks, and State‐Dependent Transaction Costs," Journal of Finance, American Finance Association, vol. 66(4), pages 1329-1368, 08.
    16. Mathieu Rosenbaum & Peter Tankov, 2011. "Asymptotically optimal discretization of hedging strategies with jumps," Papers 1108.5940, arXiv.org, revised Apr 2014.
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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.
    2. Ren Liu & Johannes Muhle-Karbe & Marko Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org.

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