Abstract:
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.
Keywords:amount of information, average cost of coding, data compression, density, entropy, Esscher transform, exponential utility, free energy, Gibbs state, interior energy, Kullback–Leibler information, mass, metastable state, minimal entropy martingale measure, Nernst theorem, pressure, relative entropy, stable state, temperature, volume.
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