Financial support from the RFBR Grant 18-31-20031 is gratefully acknowledged.
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The aim of this work is to extend the classical theory of growth-optimal investments (Shannon, Kelly, Breiman, Algoet, Cover and others) to models of asset markets with frictions—transaction costs and portfolio constraints. As the modelling framework, we use discrete-time dynamical systems generated by convex homogeneous multivalued operators in spaces of random vectors—von Neumann–Gale dynamical systems. The main results are concerned with the construction and characterization of investment strategies possessing properties of asymptotic growth-optimality almost surely.