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Nonlinear averages in economics. (English. Russian original) Zbl 1153.91429
Math. Notes 78, No. 3, 347-363 (2005); translation from Mat. Zametki 78, No. 3, 377-395 (2005).
Summary: Kolmogorov nonlinear averaging is complemented by a natural axiom. For this averaging, we prove a theorem on large deviations as well as establish the relationship to the tunnel canonical operator.

91B24 Microeconomic theory (price theory and economic markets)
60F10 Large deviations
Full Text: DOI
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[2] V. P. Maslov, ”Axioms of nonlinear averaging in financial mathematics and stock-price dynamics,” Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 48 (2003), no. 4, 800–810. · Zbl 1089.91026
[3] ”’Zero Intelligence’ Trading Closely Mimics Stock Market,” in: http://www.newscientist.com/ article.ns?id=dn6948, Katharine Davis, 05/02/01; see also other sites with reference to ”Zero Intelligence.”
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[9] V. P. Maslov, ”Integral equations and phase transitions in probabilistic games: Analogy with statistical physics,” Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 48 (2003), no. 2, 482–502.
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[14] V. P. Maslov, ”A quasistable economy and its connection with the thermodynamics of a superfluid: A default as a phase transition of zeroth kind. 1,” Survey of Applied and Industrial Mathematics, 11 (2004), no. 4, 690–732; 12 (2005), no. 1, 3–40. · Zbl 1059.91064
[15] V. N. Baturin, S. G. Lebedev, V. P. Maslov, B. I. Sadovnikov, and A. Chebotarev, ”Reconstruction of the Pareto distribution in the domain of high incomes,” Russian Economic Science of Current Interest (2005), no. 3.
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[17] V. P. Maslov, ”Capitalistic mathematics,” in: Manuscript at www.viktor-maslov.narod.ru, 2005.
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