  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.
