Entropy-Maximizing Dynamics of Continuous Markets

Abstract: By assuming the existence of the growth optimal portfolio (GOP), the stationarity of GOP-volatilities, and the maximization of relative entropy, the paper applies the benchmark approach to the modeling of the long-term dynamics of continuous markets. It reveals conservation laws, where the GOP is shown to follow a time-transformed squared Bessel process of dimension four. Moreover, it predicts the convergence of the averages of the GOP-volatilities with respect to the driving independent Brownian motions toward a common level.