Volume 3 • Issue 1 | March 2019
Quantum Probability based Decision Making in Finance: from Individual Preferences to Market Outcomes
Polina Khrennikova
Behavioural finance
Belief state
Complementary of observables
Decision operator
Disposition effect
Interference effects
Investor sentiment
Quantum probability
Subjective expected utility
Abstract:
This paper surveys the main directions of the applications in finance of a generalized probability calculus that is derived from the axiomatics of quantum physics, see monographs by [33], [12], [22]. Recently, subjective expected utility with QP (quantum probability) measures of agents’ uncertainty and contextuality in preferences was formalized in [3]. The projective measurement scheme that is at the core of QP relaxes some of the core axioms of classical probability, namely the commutativity and distributivity of events. Hence, QP captures well real decision making scenarios, where agents can have ambiguous and state dependent beliefs. In [8] agents’ make comparison between lotteries and interference effects between prospects are present that denote risk perceptions from the ambiguity about prospect realisation in the selection process. The notion of non-commuting lottery observables has the substantial to explain paradoxical behaviour of individual investors, characterised my myopia in asset return evaluation, as well as inter-asset valuation. Moreover, the interference term of agents’ comparison state can provide a quantitative description of the disposition effect from agents’ contextual utility perception. Some of the implications of non-classicality in beliefs for the composite market outcomes can be also modelled with the aid of QP. For instance, the emergence of speculative bubbles from investors’ sentiment in asset pricing is elaborated in [36, 37]
JEL classification: D01, D53, D81, D83, D84, G40