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Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints

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  • Johannes Muhle-Karbe
  • Ren Liu
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    Abstract

    An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities, in the presence of small transaction costs and a binding exogenous portfolio constraint. We explicitly derive the optimal trading policy, its welfare, and implied trading volume. As an application, we study the problem of selecting a prime broker among alternatives with different lending rates and margin requirements. Moreover, we discuss how changing regulatory constraints affect the deposit rates offered for illiquid loans.

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    File URL: http://arxiv.org/pdf/1205.4588
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.4588.

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    Date of creation: May 2012
    Date of revision: Jan 2013
    Handle: RePEc:arx:papers:1205.4588

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    Web page: http://arxiv.org/

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    1. Loewenstein, Mark, 2000. "On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 209-228, March.
    2. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    3. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    4. 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.
    5. 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.
    6. Grossman, Sanford J. & Vila, Jean-Luc, 1992. "Optimal Dynamic Trading with Leverage Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(02), pages 151-168, June.
    7. Attila Herczegh & Vilmos Prokaj, 2011. "Shadow price in the power utility case," Papers 1112.4385, arXiv.org.
    8. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    9. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    10. 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.
    11. 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.
    12. Dai, Min & Jin, Hanqing & Liu, Hong, 2011. "Illiquidity, position limits, and optimal investment for mutual funds," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1598-1630, July.
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