A new research paper proves mathematically what we already suspect: human behavior can be unpredictable. The key to the result is construction of a behavioral operator that transforms probability domains while utilizing someone's prior source of belief. Asymptotic expansion of the veritable random integral operator (a Volterra equation of the first kind), produces an ergodic sample function for confidence. Computer simulations of the model show that the sample functions mimic trends in Gallup Daily Economic Confidence Index. The ergodic nature of confidence, together with "topological mixing" and prior beliefs support a dynamical system of behavioral chaos. That explains the poor performance of long run economic and financial forecasts. 

Among other things, the model was applied to split the VIX into its hope and fear component sets, and to estimate a "confidence beta" on each set. That set the stage for arbitrage between the risk profiles on each set based on confidence beta. The paper is loaded with other examples--including a trading algorithm. Those interested can obtain a copy at A Confidence Representation Theorem for Ambiguity Aversion with App...