This thesis provides a study on the theory of stochastic von Neumann-Gale dynamical systems and their applications in Economics and Finance. This is a class of multivalued dynamical systems possessing certain properties of convexity and homogeneity. Dynamic models of this kind were originally studied by von Neumann (1937) in his pioneering work on economic growth. Recently it has been discovered that such dynamical systems provide a convenient and natural framework for the modeling of financial markets with "frictions" (transaction costs and trading constraints). Studies in this thesis develop this idea and aim, in particular, at building capital growth theory for financial markets with frictions in the framework of von Neumann-Gale dynamical systems. A characteristic feature of this class is that it deals with state spaces represented by general cones of random vectors, not necessarily coinciding with the standard non-negative cones (as is the case in the economic, rather than financial, applications). In financial terms, this means that models at hand describe financial markets where short selling is allowed.