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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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