On Minimization and Maximization of Entropy in Various Disciplines

This paper deals with some problems related to the relative entropy minimization under linear constraints. We discuss the relation between this problem and statistical physics, information theory, and financial mathematics. Furthermore, in financial mathematics we provide the explicit form of the minimal entropy martingale measure in the general discrete-time asset price model. We also give the explicit solution of the problem of the exponential utility maximization in the general discrete-time asset price model.