This paper introduces decision-making and risk-measure models based on advanced quantum theory, which address the contextuality of decisions more flexibly than previous approaches. Contextuality affects how risk is perceived, and changes in decision-making are modeled using quantum time evolution and weak values. Numerical simulations reveal that the weak value model captures contextual shifts in risk magnitude in both directions—amplification and reduction—which cannot be expressed by simple projection or time evolution alone. Empirical applications include moral hazard and inverse moral hazard, where contextuality renders the risk either more or less severe, such as governmental monetary aids examples.
Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. PhysicalReviewLetters, 83, 3077-3080. https://doi.org/10.1103/physrevlett.83.3077
[3]
Guevara, E. (2007) Quantum Econophysics Conference: Quantum Interaction. The 2007 AAAI Spring Symposium, Stanford, 26-28 March 2007, Technical Report SS-07-08.
[4]
Cheon, T. and Iqbal, A. (2008) Bayesian Nash Equilibria and Bell Inequalities. JournalofthePhysicalSocietyofJapan, 77, Article ID: 024801. https://doi.org/10.1143/jpsj.77.024801
[5]
Cheon, T. and Tsutsui, I. (2006) Classical and Quantum Contents of Solvable Game Theory on Hilbert Space. PhysicsLettersA, 348, 147-152. https://doi.org/10.1016/j.physleta.2005.08.066
[6]
Cheon, T. and Takahashi, T. (2010) Interference and Inequality in Quantum Decision Theory. PhysicsLettersA, 375, 100-104. https://doi.org/10.1016/j.physleta.2010.10.063
[7]
Aerts, D., Sassoli de Bianchi, M., Sozzo, S. and Veloz, T. (2021) Modeling Human Decision-Making: An Overview of the Brussels Quantum Approach. FoundationsofScience, 26, 27-54. https://doi.org/10.1007/s10699-018-9559-x
[8]
Eichberger, J. and Pirner, H.J. (2017) Decision Theory with a Hilbert Space as Possibility Space. Discussion Paper Series, No. 637, University of Heidelberg. https://archiv.ub.uniheidelberg.de/volltextserver/23388/1/dp637.pdf
[9]
Ellsberg, D. (1961) Risk, Ambiguity, and the Savage Axioms. TheQuarterlyJournalofEconomics, 75, 643-669. https://doi.org/10.2307/1884324
[10]
Ashtiani, M. and Azgomi, M.A. (2015) A Survey of Quantum-Like Approaches to Decision Making and Cognition. Mathematical Social Sciences, 75, 49-80. https://doi.org/10.1016/j.mathsocsci.2015.02.004
[11]
Whittle-Walls, G. (2026) A Quantum Probabilistic Framework for Reasoning Coherence under Contextual Variability. Frontiers in Cognition, 5, Article ID: 1727891. https://doi.org/10.3389/fcogn.2026.1727891
[12]
Gliner, W. (2000) Quantum Mechanics. Springer.
[13]
Yamashita, M. (2025) Quantum Risk Measures: A Consideration from Quantum Theory. Keiei Ronshu, 105, Toyo University.
[14]
Pothos, E.M. and Busemeyer, J.R. (2013) Can Quantum Probability Provide a New Direction for Cognitive Modeling? Behavioral and Brain Sciences, 36, 255-274. https://doi.org/10.1017/s0140525x12001525
[15]
Bruza, P.D., Wang, Z. and Busemeyer, J.R. (2015) Quantum Cognition: A New Theoretical Approach to Psychology. Trends in Cognitive Sciences, 19, 383-393. https://doi.org/10.1016/j.tics.2015.05.001
[16]
Yamashita, M. (2024) Quantum Mechanics Approach for Risk Aversion, Prudence, and Temperance. Journal of Mathematical Finance, 14, 130-142. https://doi.org/10.4236/jmf.2024.141007
[17]
Aharonov, Y., Albert, D.Z. and Vaidman, L. (1988) How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to Be 100. Physical Review Letters, 60, 1351-1354. https://doi.org/10.1103/physrevlett.60.1351
[18]
Aharonov, Y., Popescu, S. and Tollaksen, J. (2010) A Time-Symmetric Formulation of Quantum Mechanics. Physics Today, 63, 27-32. https://doi.org/10.1063/1.3518209
[19]
Rosales-Zárate, L., Opanchuk, B. and Reid, M.D. (2018) Weak Measurements and Quantum Weak Values for NOON States. Physical Review A, 97, Article ID: 032123. https://doi.org/10.1103/physreva.97.032123
[20]
Chen, G., Yin, P., Zhang, W.-H., Li, G.-C., Li, C.-F. and Guo, G.-C. (2021) Beating Standard Quantum Limit with Weak Measurement. Entropy, 23, Article No. 354. https://doi.org/10.3390/e23030354
[21]
Zhu, X., Zhang, Y., Pang, S., Qiao, C., Liu, Q. and Wu, S. (2011) Quantum Measurements with Preselection and Postselection. Physical Review A, 84, Article ID: 052111. https://doi.org/10.1103/physreva.84.052111
[22]
Dressel, J., Malik, M., Miatto, F.M., Jordan, A.N. and Boyd, R.W. (2014) Colloquium: Understanding Quantum Weak Values: Basics and Applications. Reviews of Modern Physics, 86, 307-316. https://doi.org/10.1103/revmodphys.86.307
[23]
Pati, A.K., Singh, U. and Sinha, U. (2015) Measuring Non-Hermitian Operators via Weak Values. Physical Review A, 92, Article ID: 052120. https://doi.org/10.1103/physreva.92.052120
[24]
Ferrie, C. and Combes, J. (2014) Weak Value Amplification Is Suboptimal for Estimation and Detection. Physical Review Letters, 112, Article ID: 040406. https://doi.org/10.1103/physrevlett.112.040406
[25]
Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999) Coherent Measures of Risk. Mathematical Finance, 9, 203-228. https://doi.org/10.1111/1467-9965.00068
[26]
Föllmer, H. and Knispel, T. (2013) Convex Risk Measures: Basic Facts, Law-Invariance and Beyond, Asymptotics for Large Portfolios. In: MacLean, L.C. and Ziemba, W.T., Eds., Handbook of the Fundamentals of Financial Decision Making, Part II, World Scientific, 507-554. https://doi.org/10.1142/9789814417358_0030
[27]
Jouini, E., Schachermayer, W. and Touzi, N. (2008) Optimal Risk Sharing for Law Invariant Monetary Utility Functions. Mathematical Finance, 18, 269-292. https://doi.org/10.1111/j.1467-9965.2007.00332.x
[28]
Kusuoka, M. (2016) Measuring Financial Risks: One Period Mode. Institute of Actuaries of Japan and CERA Seminar 2016.
[29]
Mastrogiacomo, E. and Gianin, E.R. (2015) Pareto Optimal Allocations and Optimal Risk Sharing for Quasiconvex Risk Measures. Mathematics and Financial Economics, 9, 149-167. https://doi.org/10.1007/s11579-014-0139-8
[30]
Ravanelli, C. and Svindland, G. (2014) Comonotone Pareto Optimal Allocations for Law Invariant Robust Utilities on L1. Finance and Stochastics, 18, 249-269. https://doi.org/10.1007/s00780-013-0214-7
[31]
Rockafellar, R.T. (2007) Coherent Approaches to Risk in Optimization under Uncertainty. In: OR Tools and Applications: Glimpses of Future Technologies, INFORMS, 38-61. https://doi.org/10.1287/educ.1073.0032
[32]
Pettersson-Lidbom, P. (2010) Dynamic Commitment and the Soft Budget Constraint: An Empirical Test. AmericanEconomicJournal: EconomicPolicy, 2, 154-179. https://doi.org/10.1257/pol.2.3.154
[33]
Beetsma, R., Cima, S. and Cimadomo, J. (2021) Fiscal Transfers without Moral Hazard? The International Journal of Central Banking, 17, 95-153. https://www.ijcb.org/journal/v17n3/fiscal-transfers-without-moral-hazard
[34]
Van Rompuy, H., Barroso, J.M., Juncker, J.-C. and Draghi, M. (2012) Towards a Genuine Economic and Monetary Union. European Council, December 5. https://www.consilium.europa.eu/media/23818/134069.pdf