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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 4, Pages 800–810 (Mi tvp258)  

This article is cited in 13 scientific papers (total in 13 papers)

Short Communications

Nonlinear averaging axioms in financial mathematics and stock price dynamics

V. P. Maslov

M. V. Lomonosov Moscow State University

Abstract: In the presence of an uncertainty factor, that is, if some variable $X$ assumes several values $x_1,\ldots, x_n$ rather than a single value, one usually performs an averaging over these values with some coefficients (measures) $\alpha_i$ such that $\sum_{i=1}^n\alpha_i=1$ and sets $y=\sum\alpha_ix_i$. For an equity market, there arises a nonlinear averaging for $y$. We consider an averaging of the form $f(y)=\sum\alpha_if_i(x_i)$. Starting from four natural axioms, we prove that either the above-mentioned linear averaging holds, or $y=\log\sum_{i=1}^ne^{x_i}$. An example of a stock price breakout under this summation is given.

Keywords: expectation, uncertainty factor, value of a random variable, profit, bank, stock, financial dynamics, stock price breakout.

DOI: https://doi.org/10.4213/tvp258

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English version:
Theory of Probability and its Applications, 2004, 48:4, 723–733

Bibliographic databases:

Received: 20.10.2003

Citation: V. P. Maslov, “Nonlinear averaging axioms in financial mathematics and stock price dynamics”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 800–810; Theory Probab. Appl., 48:4 (2004), 723–733

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Zeroth-Order Phase Transitions”, Math. Notes, 76:5 (2004), 697–710  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. P. Maslov, “Nonlinear financial averaging, the evolution process, and laws of econophysics”, Theory Probab. Appl., 49:2 (2005), 221–244  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Maslov V.P., “Quasistable economics and its relationship to the thermodynamics of superfluids. Default as a zero order phase transition”, Russ. J. Math. Phys., 11:4 (2004), 429–455  mathscinet  zmath  isi
    4. Maslov V.P., “Quasistable economics and its relationship to the thermodynamics of superfluids. Default as a zero order phase transition”, Russ. J. Math. Phys., 11:3 (2004), 308–334  mathscinet  zmath  isi
    5. Maslov V.P., “An evolution process leading to financial averaging and Gibbs distribution in the limit”, Dokl. Math., 70:1 (2004), 531–534  mathnet  mathscinet  zmath  isi
    6. Maslov A.V.P., “Expenditures of purchasers and turnover rate under a nonlinear financial averaging: Laws of economic physics”, Dokl. Math., 69:3 (2004), 348–351  mathnet  mathscinet  zmath  isi
    7. Maslov V.P., “The dependence of the purchasing capability and average income of a population on the number of purchasers at specialized markets and in the region. Laws of economic physics”, Dokl. Math., 69:2 (2004), 183–187  mathnet  mathscinet  zmath  isi
    8. V. P. Maslov, “Nonlinear Averages in Economics”, Math. Notes, 78:3 (2005), 347–363  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Maslov V.P., “Quantum economics”, Russ. J. Math. Phys., 12:2 (2005), 219–231  mathscinet  zmath  isi  elib
    10. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, 2009, 239–279  crossref  mathscinet  zmath  isi
    11. Kostin V.A., Kostin A.V., Kostin D.V., “Nonlinear Averaging Function of Maslov and Mathematical Models in Economics”, Dokl. Math., 87:2 (2013), 167–170  crossref  mathscinet  zmath  isi  elib  scopus
    12. Zegarlinski B., “Linear and Nonlinear Dissipative Dynamics”, Rep. Math. Phys., 77:3 (2016), 377–397  crossref  mathscinet  zmath  isi  elib  scopus
    13. Koroliuk D.V. Koroliuk V.S., “A Difference Diffusion Model With Two Equilibrium States”, Cybern. Syst. Anal., 53:6 (2017), 914–924  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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