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Homogenization and Asymptotics for Small Transaction Costs

Author

Listed:
  • Halil Mete Soner

    (ETH Zürich, Ecole Polytechnique Fédérale de Lausanne, and Swiss Finance Institute)

  • Nizar Touzi

    (Ecole Polytechnique, Paris)

Abstract

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.

Suggested Citation

  • Halil Mete Soner & Nizar Touzi, 2012. "Homogenization and Asymptotics for Small Transaction Costs," Swiss Finance Institute Research Paper Series 12-13, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1213
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    Citations

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    Cited by:

    1. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
    2. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
    3. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org, revised Sep 2014.
    4. Maxim Bichuch, 2014. "Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment," Finance and Stochastics, Springer, vol. 18(3), pages 651-694, July.
    5. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    6. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    7. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    8. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    9. Jose V. Alcala & Arash Fahim, 2013. "Balancing small fixed and proportional transaction cost in trading strategies," Papers 1304.7562, arXiv.org.
    10. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    11. Jan Kallsen & Johannes Muhle-Karbe, 2012. "Option Pricing and Hedging with Small Transaction Costs," Papers 1209.2555, arXiv.org, revised Dec 2012.
    12. Arash Fahim & Wan-Yu Tsai, 2017. "A Numerical Scheme for A Singular control problem: Investment-Consumption Under Proportional Transaction Costs," Papers 1711.01017, arXiv.org.
    13. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    14. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.

    More about this item

    Keywords

    transaction costs; homogenization; viscosity solutions; asymptotic expansions;
    All these keywords.

    JEL classification:

    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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