HIGH-DIMENSIONAL PORTFOLIO OPTIMIZATION WITH TRANSACTION COSTS

Mark Broadie () and Weiwei Shen
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Mark Broadie: Graduate School of Business, Columbia University, New York, NY 10027, USA
Weiwei Shen: Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 04, 1-49

Abstract: This paper studies Merton’s portfolio optimization problem with proportional transaction costs in a discrete-time finite horizon. Facing short-sale and borrowing constraints, investors have access to a risk-free asset and multiple risky assets whose returns follow a multivariate geometric Brownian motion. Lower and upper bounds for optimal solutions up to the problem with 20 risky assets and 40 investment periods are computed. Three lower bounds are proposed: the value function optimization (VF), the hyper-sphere and the hyper-cube policy parameterizations (HS and HC). VF attacks the conundrums in traditional value function iteration for high-dimensional dynamic programs with continuous decision and state spaces. HS and HC respectively approximate the geometry of the trading policy in the high-dimensional state space by two surfaces. To evaluate lower bounds, two new upper bounds are provided via a duality method based on a new auxiliary problem (OMG and OMG2). Compared with existing methods across various suites of parameters, new methods lucidly show superiority. The three lower bound methods always achieve higher utilities, HS and HC cut run times by a factor of 100, and OMG and OMG2 mostly provide tighter upper bounds. In addition, how the no-trading region characterizing the optimal policy deforms when short-sale and borrowing constraints bind is investigated.

Keywords: Portfolio optimization; transaction costs; value function iteration; approximate dynamic programming; lower and upper bounds (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024916500254

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