The von Neumann-Gale growth model and its Stochastic generalization

Von Neumann’s [60] model of an expanding economy, generalized by Gale [30],was one of the first models in Mathematical Economics that served as thebasis for a rich and interesting theory. This theory was developed for the mostpart in the 1950s and 1960s. Substantial contributions to it were made by suchoutstanding economists and mathematicians as McKenzie, Radner, Rockafellar,Nikaido, Morishima and others (see, e.g., the monograph by Nikaido [47] andreferences therein). The theory of the von Neumann–Gale model, in its classical form, is purely deterministic. It does not reflect the influence of random factors on economic growth. The importance of taking these factors into account was realized early on. First attempts aimed at the construction of stochastic analogues of the von Neumann–Gale model were undertaken in the 1970s by Radner [50, 51]. However, the initial attack on the problem left many questions unanswered. Studies in this direction faced serious mathematical diffculties. To overcome these diffculties, new mathematical techniques were required, that were developed only during the last decade. The main purpose of the present paper is toprovide an account of recent achievements in the field.