Optimal Portfolio Selection Under Concave Price Impact
- University of Southern California, Department of Mathematics (United States)
- City University of Hong Kong, Department of Mathematics (Hong Kong)
- Chongqing University, School of Economics and Business Administration (China)
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.
- OSTI ID:
- 22156271
- Journal Information:
- Applied Mathematics and Optimization, Vol. 67, Issue 3; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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