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Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs

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  • Andrew Papanicolaou
  • Shiva Chandra

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 $\epsilon$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrt\epsilon$. 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.

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  • Andrew Papanicolaou & Shiva Chandra, 2019. "Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs," Papers 1910.06463, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:1910.06463
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    References listed on IDEAS

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    1. Peter Bank & Mete Soner & Moritz Vo{ss}, 2015. "Hedging with Temporary Price Impact," Papers 1510.03223, arXiv.org, revised Jul 2016.
    2. Peter Bank & Halil Mete Soner & Moritz Voss, 2016. "Hedging with Temporary Price Impact," Swiss Finance Institute Research Paper Series 16-72, Swiss Finance Institute.
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