Controlled random fields, von Neumann-Gale dynamics and multimarket hedging with risk

We develop a model of asset pricing and hedging for interconnected financial markets with frictions - transaction costs and portfolio constraints. The model is based on a control theory for random fields on a directed graph. Market dynamics are described by using von Neumann-Gale dynamical systems first considered in connection with the modelling of economic growth [13,24]. The main results are hedging criteria stated in terms of risk-acceptable portfolios and consistent price systems, extending the classical superreplication criteria formulated in terms of equivalent martingale measures. © 2013 Copyright Taylor and Francis Group, LLC.