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Singular Perturbation Expansion For Utility Maximization With Order-𝜖 Quadratic Transaction Costs

Author

Listed:
  • SHIVA CHANDRA

    (Department of Finance and Risk Engineering, NYU Tandon School of Engineering, Brooklyn NY, USA)

  • ANDREW PAPANICOLAOU

    (Department of Finance and Risk Engineering, NYU Tandon School of Engineering, Brooklyn NY, USA)

Abstract

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order 𝜖 small, which leads to the optimization problem having an asymptotically-singular Hamilton–Jacobi–Bellman equation whose solution can be expanded in powers of 𝜖. In this paper, we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

Suggested Citation

  • Shiva Chandra & Andrew Papanicolaou, 2019. "Singular Perturbation Expansion For Utility Maximization With Order-𝜖 Quadratic Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-18, November.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:07:n:s0219024919500390
    DOI: 10.1142/S0219024919500390
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, October.
    2. Jean-Pierre Fouque & George Papanicolaou & K. Ronnie Sircar, 2001. "From The Implied Volatility Skew To A Robust Correction To Black-Scholes American Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 651-675.
    3. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    4. Nicolae Gârleanu & Lasse Heje Pedersen, 2013. "Dynamic Trading with Predictable Returns and Transaction Costs," Journal of Finance, American Finance Association, vol. 68(6), pages 2309-2340, December.
    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    6. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    7. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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