Financial Friction and Multiplicative Markov Market Game

Details Financial Friction and Multiplicative Markov Market Game Financial Friction and Multiplicative Markov Market Game

1999-08-18

arxiv.org/abs/cond-mat/9908253v1

IJTAF Vol. 3, No. 3 (2000), 501-510

Physics

Condensed Matter

Statistical Mechanics

10 pages, invited talk at the European Physical Society conference 'Applications of Physics in Financial Analysis', Trinity Co

Scientific paper

10.1142/S0219024900000486

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.

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