Abstract
Contextual decisions and beliefs and their impact upon market outcomes are at the core of research in behavioural finance. We describe some of the notable probabilistic fallacies that underpin investor behaviour and the consequent deviation of asset prices from the rational expectations equilibrium. In real financial markets, the complexity of financial products and the surrounding ambiguity calls for a more general formalization of agents belief formation than offered by the standard probability theory and dynamic models based on classical stochastic processes. The main advantage of quantum probability (QP) is that it can capture contextuality of beliefs through the notion of non-commuting prospect observables. QP has the potential to model myopia in asset return evaluation, as well as inter-asset valuation. Moreover, the interference term of the agents’ comparison state can provide a quantitative description of their vacillating ambiguity perception characterized by non-additive beliefs of agents. Some of the implications of non-classicality in beliefs for the composite market outcomes can also be modelled with the aid of QP. As a final step we also discuss the contributions of the growing body of psychological studies that reveal a true (quantum type) contextuality in human preference statistics showing that the classical probability theory is too restrictive to capture the very strong non-classical correlations between preference outcomes and beliefs.
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Notes
- 1.
The interested reader is referred to core texts in finance, e.g. Bodie et al. (2014).
- 2.
A comprehensive account of theoretical frameworks of ambiguity aversion in human preference formation can be found in a monograph by Gilboa (2009).
- 3.
For simplicity we devise only two eigenvectors \(|\alpha _{+}\rangle \) and \(|\alpha _{-}\rangle \), corresponding to eigenvalues \(a=\pm 1\). These projectors can be for instance beliefs about a price increase, or price decrease in the next trading period.
- 4.
Before the agents have elicited their beliefs that inform their trading behaviour, they are in a superposition state and their beliefs’ distribution is not classical.
- 5.
We note that the prices reflect agents’ beliefs about fundamentals and not the objective information that the prices would contain. Given that agents’ beliefs are contextual, these prices can deviate from the fundamental values.
- 6.
See for instance the framework by Scheinkman and Xiong (2003) and references herein.
- 7.
Under some assumptions on agents’ risk neutrality, short sales etc, we can align the QP framework with CP based frameworks on asset trading under divergence of beliefs.
- 8.
In physics such a contextual disturbance on a system is known as “signalling”.
- 9.
Cognitive experiments are performed on two pairs of questions related to measurement of four random variables. Some of the questions cannot be answered jointly, showing contextuality of human judgements, see first experiments by Asano et al. (2014), Conte et al. (2008). These experiments were followed by other controlled experiments, including different combinations of random variables and their outcomes, Cervantes and Dzhafarov (2018, (2019). A recent experiment by Basieva et al. (2019) offers evidence that there is contextuality in human judgements that cannot be captured with the aid of CP calculus.
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Khrennikova, P., Haven, E. (2021). A QP Framework: A Contextual Representation of Agents’ Preferences in Investment Choice. In: Ngoc Thach, N., Kreinovich, V., Trung, N.D. (eds) Data Science for Financial Econometrics. Studies in Computational Intelligence, vol 898. Springer, Cham. https://doi.org/10.1007/978-3-030-48853-6_7
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