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Article

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

Evstigneev I., Zhitlukhin M.

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.