This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained by large deviations estimates on empirical measures of the price process and by a generalization of the vanishing discount method to discontinuous transition operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-1,
author = {Jan Palczewski and \L ukasz Stettner},
title = {Growth-optimal portfolios under transaction costs},
journal = {Applicationes Mathematicae},
volume = {35},
year = {2008},
pages = {1-31},
zbl = {1142.91556},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-1}
}
Jan Palczewski; Łukasz Stettner. Growth-optimal portfolios under transaction costs. Applicationes Mathematicae, Tome 35 (2008) pp. 1-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-1-1/