Risk Sensitive Control of Complex Dynamical Systems

While classical models of risk in insurance and financial markets have been effectively treated by the methods of stochastic and adaptive processes, a wide variety of new technologies will require qualitatively different methods which emphasize risk due to constraints on spatial and temporal distribution of information, risk due to scale, and risk due to extreme sensitivity to changes in operating conditions. This paper explores elements of risk in complex dynamical systems which arise from sensitivity to operating conditions. It is argued that complexity based risk of this type is an essential part of what makes competitive athletics interesting. To explore this proposition, a simple interval mapping game is proposed. Analysis of the game dynamics shows that complexity based risk cannot be completely eliminated although it is possible to plan play strategies to manage it