Quantum Mechanics Approach for Risk Aversion, Prudence, and Temperance
- 1 Faculty of Business Administration, Toyo University, Tokyo, Japan
Abstract
The ideas from quantum mechanics (QM) have been used as one of problem-solving methods in the field of economics, especially in game theory and decision theory, starting about “coin flip” and “prisoner’s dilemma” and now days “decision paradoxes” . In this paper, the concept of QM is applied to prudence and temperance. Classically, risk aversion, prudence, and temperance are characterized by the risk attitude toward losses and its volatility (variance), skewness, and kurtosis as well as by utility theory, where derivatives of the utility are related to risk aversion, prudence, and temperance. Here those are treated as decision paradoxes and in the QM model, probabilities of alternatives are tentatively set as unknown and a person’s subjective probabilities toward the alternatives are set as parameterized. Investigating the utility difference before averaging can show the difference among risk aversion, prudence, and temperance. In that sense, a new QM interpretation of risk aversion, prudence, and temperance as opposed to the classical interpretation was founded in the first time.
- Meyer, D.A. (1999) Quantum Strategies. Physical Review Letters, 82, 1052-1055. https://doi.org/10.1103/PhysRevLett.82.1052
- Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. Physical Review Letters, 83, 3077-3080. https://doi.org/10.1103/PhysRevLett.83.3077
- Gliner, W. (2000) Quantum Mechanics. Springer, Germany.
- Guevara, E. (2007) Quantum Econophysics Conference: Quantum Interaction, Papers from the 2007 AAAI Spring Symposium, Technical Report SS-07-08. Stanford, California, USA.
- Cheon, T. and Iqbal, A. (2021) Bayesian Nash Equilibria and Bell Inequalities. Journal of the Physical Society of Japan, 77, 024801. https://doi.org/10.1143/JPSJ.77.024801
- Cheon, T. and Takahashi, T. (2006) Classical and Quantum Contents of Solvable Game Theory on Hilbert Space. Physics Letters A, 348, 147-152. https://doi.org/10.1016/j.physleta.2005.08.066
- Cheon, T. and Takahashi, T. (2010) Interference and Inequality in Quantum Decision Theory. Physics Letters A, 375, 100-104. https://doi.org/10.1016/j.physleta.2010.10.063
- Aerts, D., de Bianchi, M.S., Sozzo, S. and Veloz, T. (2021) Modeling Human Decision-Making: An Overview of the Brussels Quantum Approach. Foundations of Science, 26, 27-54. https://doi.org/10.1007/s10699-018-9559-x
- Ellsberg, D. (1961) Risk, Ambiguity, and the Savage Axioms. Quarterly Journal of Economics, 75, 643-669. https://doi.org/10.2307/1884324
- Eichberger, J. and Pirner, H.J. (2017) Decision Theory with a Hilbert Space as Possibility Space. Discussion Paper Series, No. 637, Heidelberg University, Heidelberg.
- Menegatti, M. (2014) New Results on the Relationship among Risk Aversion, Prudence and Temperance. European Journal of Operational Research, 232, 613-617. https://doi.org/10.1016/j.ejor.2013.08.003
- Kimball, M.S. (1990) Precautionary Savings in the Small and in the Large. Econometrica, 58, 53-73. https://doi.org/10.2307/2938334
- Leland, H.E. (1968) Saving and Uncertainty: The Precautionary Demand for Saving. Quarterly Journal of Economics, 82, 465-473. https://doi.org/10.2307/1879518
- Sandmo, A. (1970) The Effect of Uncertainty on Saving Decisions. Review of Economic Studies, 37, 353-360. https://doi.org/10.2307/2296725
- Kimball, M.S. (1992) Precautionary Motives for Holding Assets. In: Newman, P., Milgate, M. and Falwell, J., Eds., The New Palgrave Dictionary of Money and Finance, Stockton Press, New York, 158-161.