Abstract
We elaborate on various uncertainty calculi in current research efforts to improve empirical econometrics. These consist essentially of considering appropriate non additive (and non commutative) probabilities, as well as taking into account economic data which involved economic agents’ behavior. After presenting a panorama of well-known non traditional probabilistic methods, we focus on the emerging effort of taking the analogy of financial econometrics with quantum mechanics to exhibit the promising use of quantum probability for modeling human behavior, and of Bohmian mechanics for modeling economic data.
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References
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)
Baaquie, B.E.: Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, Cambridge (2007)
Bohm, D.: Quantum Theory. Prentice Hall, Englewood Cliffs (1951)
Box, G.E.P.: Science and statistics. J. Am. Stat. Assoc. 71(356), 791–799 (1976)
Box, G.E.P.: Robustness in the strategy of scientific model building. In: Launer, R.L., Wilkinson, G.N. (eds.) Robustness in Statistics, pp. 201–236. Academic Press, New York (1979)
Breiman, L.: Statistical modeling: the two cultures. Stat. Sci. 16(3), 199–215 (2001)
Briggs, W.: Uncertainty: The Soul of Modeling, Probability and Statistics. Springer, New York (2016)
Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognitive and Decision. Cambridge University Press, Cambridge (2012)
Campbell, J.Y., Lo, A.W., Mackinlay, A.C.: The Econometrics of Financial Markets. Princeton University Press, Princeton (1997)
Choustova, O.: Quantum Bohmian model for financial markets. Phys. A 347, 304–314 (2006)
Darbyshire, P.: Quantum physics meets classical finance. Phys. World 18(5), 25–29 (2005)
Dejong, D.N., Dave, C.: Structural Macroeconometrics. Princeton University Press, Princeton (2007)
De Saint Exupery, A.: The Little Prince. Penguin Books (1995)
Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)
Denneberg, D.: Non-additive Measure and Integral. Kluwer Academic Press, Dordrecht (1994)
Derman, D.: My life as a Quant: Reflections on Physics and Finance. Wiley, Hoboken (2004)
Diaconis, P., Skyrms, B.: Ten Great Ideas About Chance. Princeton University Press, Princeton and Oxford (2018)
Dirac, D.: The Principles of Quantum Mechanics. Clarendon Press, Oxford (1947)
Ellsberg, D.: Risk, ambiguity, and the savage axioms. Q. J. Econ. 75(4), 643–669 (1961)
Fegin, R., Halpern, J.Y.: Uncertainty, belief and probability. Comput. Intell. 7, 160–173 (1991)
Feynman, R.: The concept of probability in quantum mechanics. In: Berkeley Symposium on Mathematical Statistics and Probability, pp. 533–541 (1951)
Fishburn, P.C.: Non Linear Preference and Utility Theory. Wheatsheaf Books, Sussex (1988)
Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1970)
Florens, J.P., Marimoutou, V., Peguin-Feissolle, A.: Econometric Modeling and Inference. Cambridge University Press, Cambridge (2007)
Focardi, S.M.: Is economics an empirical science? If not, can it become one? Front. Appl. Math. Stat. 1, 7 (2015)
Freedman, D., Pisani, R., Purves, R.: Statistics, 4th edn. W.W. Norton, New York (2007)
Gale, R.P., Hochhaus, A., Zhang, M.J.: What is the (p-) value of the p-value? Leukemia 30, 1965–1967 (2016)
Gelman, A., Betancourt, M.: Does quantum uncertainty have a place in everyday applied statistics? Behav. Brain Sci. 36(3), 285 (2013)
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)
Gilboa, I., Postlewaite, A.W., Schmeidler, D.: Probability and uncertainty in economic modeling. J. Econ. Perspect. 22(3), 173–188 (2008)
Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2013)
Hawking, S., Mlodinow, L.: The Grand Design. Bantam Books, London (2010)
Huber, P.J.: The use of Choquet capacities in statistics. Bull. Inst. Intern. Stat. 4, 181–188 (1973)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–292 (1979)
Kreps, D.M.: Notes on the Theory of Choice. Westview Press, Boulder (1988)
Lambertini, L.: John von Neumann between physics and economics: a methodological note. Rev. Econ. Anal. 5, 177–189 (2013)
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)
Meyer, P.A.: Quantum Probability for Probabilists. Lecture Notes in Mathematics. Springer, Heidelberg (1995)
Nguyen, H.T.: On random sets and belief functions. J. Math. Anal. Appl. 65(3), 531–542 (1978)
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. 311–330. Wiley, New York (1994)
Nguyen, H.T.: An Introduction to Random Sets. Chapman and Hall/CRC Press, Boca Raton (2006)
Nguyen, H.T., Prasad, N.R., Walker, C.L., Walker, E.A.: A first Course in Fuzzy and Neural Control. Chapman and Hall/CRC Press, Boca Raton (2003)
Nguyen, H.T.: On evidence measures of support for reasoning with integrated uncertainty: a lesson from the ban of p-values in statistical inference. In: Huynh, V.N., et al. (eds.) Integrated Uncertainty in Knowledge Modeling and Decision Making. Lecture Notes in Artificial Intelligence, vol. 9978, pp. 3–15. Springer, Cham (2016)
Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic, 3rd edn. Chapman and Hall/CRC Press, Boca Raton (2006)
Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Springer, Basel (1992)
Puhalskii, A.: Large Deviations and Idempotent Probability. Chapman and Hall/CRC Press, Boca Raton (2001)
Schmeidler, D.: Integral representation without additivity. Proc. Am. Math. Soc. 97, 255–261 (1986)
Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57(3), 571–587 (1989)
Segal, W., Segal, I.E.: The Black-Scholes pricing formula in the quantum context. Proc. Natl. Acad. Sci. 95, 4072–4075 (1998)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Shmueli, G.: To explain or TP predict. Stat. Sci. 25(3), 289–310 (2010)
Soros, J.: The Alchemy of Finance: Reading of Mind of the Market. Wiley, New York (1987)
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)
Von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Wasserstein, R.L., Lazar, N.A.: The ASA’s statement on p-values: context, process and purpose. Am. Stat. 70, 129–133 (2016)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. J. Fuzzy Sets Syst. 1, 3–28 (1978)
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Nguyen, H.T., Trung, N.D., Thach, N.N. (2019). Beyond Traditional Probabilistic Methods in Econometrics. In: Kreinovich, V., Thach, N., Trung, N., Van Thanh, D. (eds) Beyond Traditional Probabilistic Methods in Economics. ECONVN 2019. Studies in Computational Intelligence, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-030-04200-4_1
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