Entropy-Maximizing Dynamics of Continuous Markets

TL;DR

This paper models the long-term dynamics of continuous markets using entropy maximization and the benchmark approach, revealing conservation laws and the behavior of the growth optimal portfolio as a squared Bessel process.

Contribution

It introduces a novel framework combining entropy maximization with the benchmark approach to analyze continuous market dynamics, highlighting new conservation laws and portfolio behaviors.

Findings

GOP follows a time-transformed squared Bessel process of dimension four

GOP-volatilities converge to a common level over time

The model predicts long-term market behavior based on entropy principles

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.