Von Neumann-Gale Dynamics and Capital Growth in Financial Markets with Frictions

Esmaeil Babaei Khezerloo, Igor Evstigneev, Klaus Reiner Schenk-Hoppé, Mikhail Zhitlukhin

Research output: Contribution to journalArticlepeer-review


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.
This paper concludes a series of publications on growth-optimal investments under transaction costs, that resolved a number of long-standing open problems. It required developing a new modeling approach and new methods of mathematical analysis.
Original languageEnglish
JournalMathematics and Financial Economics
Early online date21 Jan 2020
Publication statusPublished - 2020


  • capital growth theory
  • transaction costs
  • benchmark strategies
  • numeraire portfolios
  • random dynamical systems
  • convex multivalued operators
  • von Neumann-Gale model
  • rapid paths


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