An Invitation to Quantum Econometrics

Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 760)


We elaborate on the possibility to considering quantum probability calculus to improve statistical methods in economics in general, and in quantitative finance, in particular. A tutorial on the analogy between quantum mechanics and models in econometrics, using Kolmogorov probability theory, is given. Several research issues are mentioned.


Density matrix Hilbert spaces Kolmogorov probability calculus Observables Quantum finance Quantum mechanics Quantum probability Schrodinger wave equation Self adjoint operators Spectral measures 


  1. 1.
    Baaquie, B.E.: Quantum Finance. Cambridge University Press, Cambridge (2007)MATHGoogle Scholar
  2. 2.
    Feynman, R.: Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367–387 (1948)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Feynman, R.: The concept of probability in quantum mechanics. In: Berkeley Symposium on Mathematical Statistics and Probability, pp. 533–541 (1951)Google Scholar
  4. 4.
    Feynman, R.: The Feynman Lectures on Physics, Volume III: Quantum Mechanics. Basic Books, New York (1965)Google Scholar
  5. 5.
    Gelman, A., Bethancourt, M.: Does quantum uncertainty have a place in everyday applied statistics? Behav. Brain Sci. 36(3), 285 (2013)CrossRefGoogle Scholar
  6. 6.
    Keller, J.B., MacLaughlin, D.W.: The Feynman integral. Am. Math. Mon. 82(5), 451–465 (1975)CrossRefGoogle Scholar
  7. 7.
    Khrennikov, A.Y.: Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena. Found. Phys. 29, 1065–1098 (1999)Google Scholar
  8. 8.
    Nguyen, H.T.: An Introduction to Random Sets. Chapman and Hall/CRC Press, Boca Raton (2006)CrossRefMATHGoogle Scholar
  9. 9.
    Nguyen, H.T.: Conditional Events Algebras: The State-of-the-Art. Springer’s Kreinovich Festschrift (2017, to appear)Google Scholar
  10. 10.
    Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Birkhauser, Basel (1992)CrossRefMATHGoogle Scholar
  11. 11.
    Segal, W., Segal, I.E.: The Black-Sholes pricing formula in the quantum context. Proc. Natl. Acad. Sci. U.S.A. 95, 4072–4075 (1998)CrossRefMATHGoogle Scholar
  12. 12.
    Sethna, J.P.: Statistical Mechanics: Entropy, Order Parameters, and Complexity. Clarendon Press, Oxford (2016)MATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.New Mexico State UniversityLas CrucesUSA
  2. 2.Chiang Mai UniversityChiang MaiThailand
  3. 3.Banking UniversityHo-Chi-Minh CityVietnam

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