Optimal portfolio selection under concave price impact

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)353-390
Journal / PublicationApplied Mathematics and Optimization
Volume67
Issue number3
Publication statusPublished - Jun 2013

Abstract

In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is small. The price impact can be thought of as either a liquidity cost or a transaction cost, but the concavity nature of the cost leads to some fundamental difference from those in the existing literature. We show that the problem can be reduced to an impulse control problem, but without fixed cost, and that the value function is a viscosity solution to a special type of Quasi-Variational Inequality (QVI). We also prove directly (without using the solution to the QVI) that the optimal strategy exists and more importantly, despite the absence of a fixed cost, it is still in a "piecewise constant" form, reflecting a more practical perspective. © 2013 Springer Science+Business Media New York.

Research Area(s)

  • Impulse control, Liquidity risk, Optimal portfolio selection, Price impact, Stochastic optimization, Transaction cost

Citation Format(s)

Optimal portfolio selection under concave price impact. / Ma, Jin; Song, Qingshuo; Xu, Jing et al.
In: Applied Mathematics and Optimization, Vol. 67, No. 3, 06.2013, p. 353-390.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review