On the possibility of optimal investment

Abstract

We analyze the theory of optimal investment in risky assets, developed recently by Marsili, Maslov and Zhang [Physica A 253 (1998) 403]. When the real data are used instead of abstract stochastic process, it appears that a non-trivial investment strategy is rarely possible. We show that non-zero transaction costs make the applicability of the method even more difficult. We generalize the method in order to take into account possible correlations in the asset price.