Financial Friction and Multiplicative Markov Market Game
Abstract
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal strategies and expected frictional losses of the friction parameter. We present one derivation in terms of invariant measures of drift-diffusion processes (Fokker- Planck approach), and one derivation using the Hamilton-Jacobi-Bellman equation of optimal control theory. We also show that a significant part of the results can be derived without computation by a kind of dimensional analysis. We comment on the extension of the method to other sources of uncertainty, and discuss what conclusions can be drawn about the growth-optimal criterion as such.
Keywords
Cite
@article{arxiv.cond-mat/9908253,
title = {Financial Friction and Multiplicative Markov Market Game},
author = {Erik Aurell and Paolo Muratore-Ginanneschi},
journal= {arXiv preprint arXiv:cond-mat/9908253},
year = {2011}
}
Comments
10 pages, invited talk at the European Physical Society conference 'Applications of Physics in Financial Analysis', Trinity College, Dublin, Ireland, July 14-17, 1999