SINGULAR PERTURBATION EXPANSION FOR UTILITY MAXIMIZATION WITH ORDER-𝜖 QUADRATIC TRANSACTION COSTS

Shiva Chandra and Andrew Papanicolaou ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 07, 1-18

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.

Keywords: Transaction costs; singular perturbation expansion; stochastic control; Merton problem; aim portfolio (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500390

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