Singular Perturbation Expansion for Utility Maximization with Order-$\epsilon$ Quadratic Transaction Costs
Andrew Papanicolaou and
Papers from arXiv.org
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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Date: 2019-10, Revised 2019-11
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1910.06463
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