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Homogenization and asymptotics for small transaction costs

  • H. Mete Soner
  • Nizar Touzi
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    We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.

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    File URL: http://arxiv.org/pdf/1202.6131
    File Function: Latest version
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    Paper provided by arXiv.org in its series Papers with number 1202.6131.

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    Date of creation: Feb 2012
    Date of revision: Jun 2013
    Handle: RePEc:arx:papers:1202.6131
    Contact details of provider: Web page: http://arxiv.org/

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    1. 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.
    2. C. Atkinson & S. Mokkhavesa, 2004. "Multi-asset portfolio optimization with transaction cost," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(2), pages 95-123.
    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. Freddy Delbaen & Yuri M. Kabanov & Esko Valkeila, 2002. "Hedging under Transaction Costs in Currency Markets: a Discrete-Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 45-61.
    5. 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.
    6. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    7. 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.
    8. Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "Asymptotics and Duality for the Davis and Norman Problem," Papers 1010.0627, arXiv.org, revised Aug 2011.
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