Growth-optimal portfolios under transaction costs

Jan Palczewski¹ ; /Lukasz Stettner²

¹ School of Mathematics University of Leeds Leeds LS2 9JT, UK and Faculty of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
² Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland

Applicationes Mathematicae, Tome 35 (2008) no. 1, pp. 1-31

Résumé

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.

Détail

DOI : 10.4064/am35-1-1

Keywords: paper studies portfolio optimization problem discrete time markovian model financial market which asset price dynamics depends external process economic factors there transaction costs structure covers particular fixed plus proportional costs prove there exists self financing trading strategy maximizing average growth rate portfolio wealth strategy has markovian form result obtained large deviations estimates empirical measures price process generalization vanishing discount method discontinuous transition operators