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.

中文翻译：

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冯·诺依曼–大风的动态和金融市场中的资本增长与摩擦

这项工作的目的是将经典的增长最优投资理论（Shannon，Kelly，Breiman，Algoet，Cover等）扩展到具有摩擦的资产市场模型（交易成本和投资组合约束）。作为建模框架，我们使用由凸均质多值算子在随机向量空间中生成的离散时间动力系统-冯·诺伊曼–盖尔动力系统。主要结果与几乎肯定具有渐近增长最优性的投资策略的构建和特征有关。