Von Neumann-Gale Dynamical Systems with Applications in Finance

Igor Evstigneev (University of Manchester)
Thursday, November 3, 2011 - 4:00pm
Rudower Chaussee 25, Room 1.115

Von Neumann-Gale dynamical systems are defined in terms of multivalued operators possessing properties of convexity and homogeneity. These operators assign to each element of a given cone a convex subset of the cone describing possible one-step transitions from one state of the system to another. The classical, deterministic theory of such dynamics was originally aimed at the modelling of economic growth (von Neumann 1937 and Gale 1956). First attempts to build a stochastic generalization of this theory were undertaken in the 1970s by Dynkin, Radner and their research groups. However, the initial attack on the problem left many questions unanswered. Substantial progress was made only in the late 1990s, and final solutions to the main open problems were obtained only in the last four or five years. Recently it has been observed that stochastic analogues of von Neumann-Gale systems provide a natural and convenient framework for financial modelling (asset pricing and hedging under transaction costs). This  observation gave a new momentum to studies in the field and posed new interesting questions. The talk will give an introduction into the theory, review recent progress and discuss applications.