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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 3, Pages 466–486
DOI: https://doi.org/10.4213/tvp266 (Mi tvp266) 		 
This article is cited in 49 scientific papers (total in 49 papers)

On minimization and maximization of entropy in various disciplines

V. P. Maslov, A. S. Cherny

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (2155 kB) Citations (49)
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DOI: https://doi.org/10.4213/tvp266
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.
Received: 26.03.2003
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 3, Pages 447–464
DOI: https://doi.org/10.1137/S0040585X9798052X
Bibliographic databases:
Language: Russian
Citation: V. P. Maslov, A. S. Cherny, “On minimization and maximization of entropy in various disciplines”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 466–486; Theory Probab. Appl., 48:3 (2004), 447–464
Citation in format AMSBIB
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\by V.~P.~Maslov, A.~S.~Cherny
\paper On minimization and maximization
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\issue 3
\pages 466--486
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\zmath{https://zbmath.org/?q=an:1075.94007}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 447--464
\crossref{https://doi.org/10.1137/S0040585X9798052X}
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  • https://doi.org/10.4213/tvp266
  • https://www.mathnet.ru/eng/tvp/v48/i3/p466
    • This publication is cited in the following 49 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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