Quantum Decision Theory Series: #1 Quantum Decision Theory and Finance

journal.pone.0168045.g005

by Prof. Sudip Patra

 

This article discusses the rise of a promising paradigm in social science, namely quantum decision theory, applied to financial models in specific. A large portion of social science is based on classical decision theory which again borrows from the Kolgomorov set theory, and more deeply from the classical Boolian logic. However since late 70s a plethora of behavioral, or experimental studies have shown that predictions of classical decision theory does not explain real data, or does not capture real human decision making. The recent decade has witnessed a great uprising of an alternative decision theory based on the quantum probability theory. Specifically such so called quantum-like models have been quite successful in cognitive decision theory, as well as in other social sciences like financial decision making. The current article summarizes some of the exciting findings in the same area.

Unlike the classical political economy the neoclassical economics literature based itself centrally on the classical decision theory, which in technical terms was called as the expected utility theory (EUT). The main premise of EUT is that we human beings are fully rational, utility maximizing machines once the full information set on any scenario is available to us. In this modeling if full information is available to the rational agents then decision making and hence utility obtained from such choices can be fully determined. As if human beings can really be like the Laplace demon who if gets access to the full information about the initial conditions of the universe could predict the evolution ad infinitum without a miss. Again probabilities can enter the calculus only due to lack of information,  for example if we do not have information about all the factors (which in principle is knowable) needed to predict fully the rainfall tomorrow, then only we are allowed to model in terms of probability distribution. So randomness which we witness all around is just epistemic or pseudo randomness and deep down there is full order in the nature, and also in the human nature. Such models are then rightly called as the axiomatic models since they are based on some axioms on human preferences which if true will produce such preferences.

Certainly such a model in its pure form never was successful to predict human choices under realistic scenarios of ambiguity and uncertainties, mainly say in the financial markets which is riddled with behavioral biases. Hence later there have been modifications of the same, for example the bounded rationality model, which holds that given the incomplete information set agents are actually utility satisfiers rather than perfect utility maximizers.  Policy making paradigms have also revolved around such theoretical and philosophical models, which had deep impacts on the way policy makers viewed markets. For example the dictum : market can do no mistake, or the so called efficiency market theory is the product of such underlying idealism. We have already experienced the deep fault lines in such theories (which were all pervading from Govt policy making to Banking business to speculative asset markets) through the devastating effects of the great 2007 crisis over the globe.

Hence, the real question is whether it’s the time to rethink the very foundations of decision making theory, and its applications in finance and alike areas. From 1970s onwards we have been supplied with plethora of experimental data on human decision making which clearly violates basic principles of EUT and also classical game theory. Some of the fundamental violations are, sure thing principle violation, presence of conjunction and disjunction effects, presence of order effects  in human decision making under ambiguity or uncertainty.

Behavioural finance camp since Kahneman has provided many heuristics based models of behavior, some of them like prospect theory or the irrational exuberance model of Shiller are famous, however there are some weaknesses of such modeling. One, these models seem to be very disaggregated or its hard to see any common thread connecting such models,  and two, they fundamentally try to avoid any kind of meaningful probabilistic model of choice making at all.

It is against this background that the quantum decision theory has emerged strongly since the latter half of 90s. In the onset one should be careful not to confuse the quantum –like modeling in decision making with quantum physics as such, and nor with any spooky claims of quantum consciousness etc (it goes without saying that market is full with such nonsensical money making enterprises!). Quantum decision making is a genuine hard research based on the application of quantum probabilistic theory to the human decision making under various contexts, mainly in the contexts of ambiguity. The theory is well backed with data/ experiments, which shows surprising efficacy of quantum math on predicting closely human behavior. There are certainly brilliant minds, for example Roger Penrose at Oxford University, who are working on a physical quantum gravity brain theory, which proposes that brain activities can really be outcomes of quantum processes, but such studies are by no means conclusive.

Hence we, who work in quantum –like modeling or QDT are at best agnostic about quantum brain theory, and we use QDT as a wonderful tool to predict human behavior better, one can say this is a black box view, but we don’t want to speculate.

Briefly put there are at least two ways in which quantum –like modeling can be done in finance, one, in which following the QDT models the belief state of the agents in market scenarios, and also models how such belief states are updated based on new information arrival, and two, where the mathematical structure of ordinary quantum mechanics or more advanced quantum field theory is utilized to predict asset price behavior.

In the first approach belief states of agents are modeled according to Q-bit or quantum bit states, which means initial belief states are taken as to be superposition (as opposed to classical mixture of states) of 0 and 1 states, where 0 and 1 states may mean different beliefs about outcomes, for example price of assets rising or falling. Such states are represented by matrices / square matrices which are basically states in finite / infinite dimensional Hilbert space (for a detailed discussion of mathematical properties of Hilbert space please refer to the end references), which are endowed with inner products and self-adjoint operators. Any observable, for example an answer to a question like whether the price will rise or fall, is represented by a self adjoint operator/ Hermitian operator, such an operation reduces the initial superposition state to one of the Eigen values of the state. Hence it is possible to measure the probability of reduction of the initial superposition state to its Eigen values, and such probabilities are given by the celebrated Born’s rule as widely used in quantum physics. Along with the measurement of probabilities we can also measure the updation of belief states simultaneously. One critical point is that such updation of belief states are given by a mathematical formulation which is not Bayesian, or does not follow standard Bayesian probability updation scheme, which is better since this helps avoiding the so called zero prior trap: if the prior belief/ probabilities of any outcome is near 0 or 1 then it remains so whatever is the information supply later, however in reality we do see drastic changes in belief states in financial markets, for example think about stock market crashes! In such cases Bayesian scheme may not work fruitfully due to such zero prior problems, but Quantum probability scheme will. Another novel advantage in such scheme is understanding the uncertainty context better, and predicting choices under uncertainty better through such probability measures.

Till now we have found good evidence of real data following the predictions of QDT/ Quantum probability theory. A new paradigm is on rise. It may be your turn next to contribute.

 

References

  • Aerts, D and Aerts, S (1995), application of quantum statistics in psychological studies of decision processes, Foundations of Science1, 85-97.
  • Haven, Emmanuel and Adrei Khrennikov, ‘Quantum Social Science’, 2013, Cambridge University Press.
  • Shiller, R.J, and George Akerlof, ‘Animal Spirits’, 2009, Princeton University Press.

 

Professor Sudip Patra is an Assistant Professor of Management Practice at O.P. Jindal Global University . His research interest encompass dividend signaling theory under information asymmetry, game theory for applied corporate finance, econometric modeling, and allied areas.

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