Optimal Portfolio Selection under Concave Price Impact

Details Optimal Portfolio Selection under Concave Price Impact Optimal Portfolio Selection under Concave Price Impact

2012-04-22

arxiv.org/abs/1204.4852v1

Mathematics

Probability

38 pages

Scientific paper

In this paper we study an optimal portfolio selection problem under instantaneous price compact. Based 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 the liquidity cost or 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.

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