Geodesic
On minimization and maximization
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 466-486

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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, density, entropy, exponential utility, free energy, Gibbs state, interior energy, Kullback–Leibler information, metastable state, minimal entropy martingale measure, Nernst theorem, pressure, relative entropy, stable state, temperature
Mots-clés : data compression, Esscher transform, mass, volume. 
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     author = {V. P. Maslov and A. S. Cherny},
     title = {On minimization and maximization},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {466--486},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a2/}
}
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V. P. Maslov; A. S. Cherny. On minimization and maximization. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 466-486. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a2/