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Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs

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  • Maxim Bichuch
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    Abstract

    We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is power utility. We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of transaction cost parameter. We also obtain a "nearly optimal" strategy, whose utility asymptotically matches the leading terms in the value function.

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    File URL: http://arxiv.org/pdf/1112.2749
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    Paper provided by arXiv.org in its series Papers with number 1112.2749.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.2749

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    1. George M. Constantinides & Thaleia Zariphopoulou, . "Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs and General Preferences," CRSP working papers, Center for Research in Security Prices, Graduate School of Business, University of Chicago 347, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    2. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(2), pages 245-263, October.
    3. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(2), pages 133-165.
    4. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
    5. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, Springer, vol. 8(2), pages 181-206, 05.
    6. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, Springer, vol. 3(2), pages 237-248.
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    Cited by:
    1. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, Springer, vol. 18(1), pages 1-37, January.
    2. Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
    3. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.

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