Skip to main content

On Quantum Probability Calculus for Modeling Economic Decisions

  • Conference paper
  • First Online:
Structural Changes and their Econometric Modeling (TES 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 808))

Included in the following conference series:

Abstract

In view of the Nobel Memorial Prize in Economic Sciences awarded to Richard H. Thaler in 2017 for his work on behavioral economics, we address in this paper the fundamentals of uncertainty modeling of free will. Extensions of von Neumann’s expected utility theory in social choice, including various nonadditive probability approaches, and prospect theory seem getting closer to cognitive behavior, but still ignore an important factor in human decision-making, namely the so-called “order effect”. Thus, a better candidate for modeling quantitatively uncertainty, under which economic agents make their decisions, could be a probability calculus which is both nonadditive and noncommutative. Such a probability calculus already exists, and it is called “quantum probability”. The main goal of this paper is to elaborate on the rationale of using quantum stochastic calculus in decision-making for econometricians, in a conference such as this, who are not yet aware of this new trend of on going research in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allais, M.: Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americaine. Econometrica 21(4), 503–546 (1953)

    Article  MathSciNet  Google Scholar 

  2. Baaquie, B.E.: Quantum Finance. Cambridge University Press, Cambridge, New York (2004)

    Book  Google Scholar 

  3. Briggs, W.: Uncertainty: The Soul of Modeling, Probability and Statistics. Springer, New York (2016)

    Book  Google Scholar 

  4. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  5. Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  Google Scholar 

  6. Denneberg, D.: Non-additive Measure and Integral. Kluwer Academic Press, Dordrecht (1994)

    Book  Google Scholar 

  7. Derman, D.: My Life as a Quant: Reflections on Physics and Finance. Wiley, Hoboken (2004)

    Google Scholar 

  8. Diaconis, P., Skyrms, B.: Ten Great Ideas About Chance. Princeton University Press, Princeton (2018)

    Book  Google Scholar 

  9. Ellsberg, D.: Risk, ambiguity, and the savage axioms. Q. J. Econ. 75(4), 643–669 (1961)

    Article  Google Scholar 

  10. Fegin, R., Halpern, J.Y.: Uncertainty, belief and probability. Comput. Intell. 7, 160–173 (1991)

    Article  Google Scholar 

  11. Feynman, R.: The concept of probability in quantum mechanics. In: Berkeley Symposium on Mathematical Statistics and Probability, pp. 533–541 (1951)

    Google Scholar 

  12. Fishburn, P.C.: Non Linear Preference and Utility Theory. Wheatsheaf Books, Brighton (1988)

    MATH  Google Scholar 

  13. Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1970)

    Book  Google Scholar 

  14. Gelman, A., Betancourt, M.: Does quantum uncertainty have a place in everyday applied statistics? Behav. Brain Sci. 36(3), 285 (2013)

    Article  Google Scholar 

  15. Gilboa, I., Marinacci, M.: Ambiguity and the Bayesian paradigm. In: Acemoglu, D. (ed.) Advances in Economics and Econometrics, pp. 179–242. Cambridge University Press, Cambridge (2013)

    Chapter  Google Scholar 

  16. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  17. Hawking, S., Mlodinow, L.: The Grand Design. Bantam Books, London (2010)

    Google Scholar 

  18. Huber, P.J.: The use of Choquet capacities in statistics. Bull. Inst. Int. Stat. 4, 181–188 (1973)

    MathSciNet  Google Scholar 

  19. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–292 (1979)

    Article  Google Scholar 

  20. Kreps, D.M.: Notes on the Theory of Choice. Westview Press, Boulder (1988)

    Google Scholar 

  21. Lambertini, L.: John von Neumann between physics and economics: a methodological note. Rev. Econ. Anal. 5, 177–189 (2013)

    Google Scholar 

  22. Marinacci, M., Montrucchio, L.: Introduction to the mathematics of ambiguity. In: Gilboa, I. (ed.) Uncertainty in Economic Theory, pp. 46–107. Routledge, New York (2004)

    Chapter  Google Scholar 

  23. Meyer, P.A.: Quantum Probability for Probabilists. Lecture Notes in Mathematics. Springer, Heidelberg (1995)

    Book  Google Scholar 

  24. Nguyen, H.T.: On random sets and belief functions. J. Math. Anal. Appl. 65(3), 531–542 (1978)

    Article  MathSciNet  Google Scholar 

  25. Nguyen, H.T., Walker, A.E.: On decision making using belief functions. In: Yager, R., Kacprzyk, J., Pedrizzi, M. (eds.) Advances the Dempster-Shafer Theory of Evidence, pp. 331–330. Wiley, New York (1994)

    Google Scholar 

  26. Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Springer, Basel (1992)

    MATH  Google Scholar 

  27. Schmeidler, D.: Integral representation without additivity. Proc. Am. Math. Soc. 97, 255–261 (1986)

    Article  MathSciNet  Google Scholar 

  28. Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57(3), 571–587 (1989)

    Article  MathSciNet  Google Scholar 

  29. Segal, W., Segal, I.E.: The Black-Scholes pricing formula in the quantum context. Proc. Nat. Acad. Sci. 95, 4072–4075 (1998)

    Article  Google Scholar 

  30. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  31. Sriboonchitta, S., Wong, W.K., Dhompongsa, S., Nguyen, H.T.: Stochastic Dominance and Applications to Finance, Risk and Economics. Chapman and Hall/CRC Press, Boca Raton (2010)

    MATH  Google Scholar 

  32. Von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    MATH  Google Scholar 

  33. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)

    Book  Google Scholar 

  34. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. J. Fuzzy Sets Syst. 1, 3–28 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hung T. Nguyen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nguyen, H.T., Sriboonchitta, S., Thach, N.N. (2019). On Quantum Probability Calculus for Modeling Economic Decisions. In: Kreinovich, V., Sriboonchitta, S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham. https://doi.org/10.1007/978-3-030-04263-9_2

Download citation

Publish with us

Policies and ethics