UTILITY MAXIMIZATION IN A BINOMIAL MODEL WITH TRANSACTION COSTS: A DUALITY APPROACH BASED ON THE SHADOW PRICE PROCESS

Christian Bayer () and Bezirgen Veliyev
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Christian Bayer: Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 04, 1-27

Abstract: We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be made explicit for small transaction costs (in the sense of an asymptotic expansion). Here we find that, contrary to the classical results in continuous time, see Janeček and Shreve (2004), Finance and Stochastics 8, 181–206, the size of the no-trade-region as well as the asymptotic growth rate depend analytically on the level λ of transaction costs, implying a linear first-order effect of perturbations of (small) transaction costs, in contrast to effects of orders λ1/3 and λ2/3, respectively, as in continuous time models. Following the recent study by Gerhold et al. (2013), Finance and Stochastics 17, 325–354, we obtain the asymptotic expansion by an almost explicit construction of the shadow price process.

Keywords: Utility maximization; binomial model; transaction costs; duality methods (search for similar items in EconPapers)
Date: 2014
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Working Paper: Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process (2012)
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DOI: 10.1142/S0219024914500228

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