Asset trading under non-classical ambiguity and heterogeneous beliefs

We propose discrete time asset trading framework based on quantum probability formalism that represents well the ambiguity of agents in respect to the fundamental values and price states of the traded assets. Divergence of beliefs alike classical finance frameworks (e.g. works by Harrison and Kreps, (1978); Scheinkman and Xiong, (2003)) produces different expectations of agents about the future price distribution of the traded risky asset. The model accounts for the emergence of heterogeneous beliefs from agents’ ambiguity about both the future asset price states and the fundamentals, as opposed to the strands that attribute heterogeneous beliefs to asymmetric information and different, yet firm prior beliefs about stochastic processes over fundamentals. The introduced quantum probability paradigm allows to depict a genuine ambiguity of agents in respect to the future realization of payoff relevant variables and prices. There are two sources of ambiguity: (i) the imperfect market knowledge of agents, manifest in a divergence of ambiguous priors, (ii) uncertainty about the probability distribution of price states and dividends in the next trading period. Agents update their beliefs via Born rule (instead of Bayesian update) when observing the realizedprice outcomes and dividend signals. An important feature relates to individual traders’ not possessing a joint probability distribution over the payoff relevant variables and price outcomes that brings up attraction, respective aversion to ambiguity in their interpretation of public signals. On the level of the composite model of stock exchange, formed by the expectations of two ensembles of agents, an interference term can serve as a quantitative testable prediction in respect to the excess volatility of asset prices created by traders’ optimistic and pessimistic beliefs

A QP Framework: A Contextual Representation of Agents’ Preferences in Investment Choice

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

Quantum-like model of subjective expected utility: A survey of applications to finance

In this survey paper we review the potential financial applications of quantum probability (QP) framework of subjective expected utility formalized in [2]. The model serves as a generalization to the classical probability (CP) scheme and relaxes the core axioms of commuta-tivity and distributivity of events. The agents form subjective beliefs via the rules of projective probability calculus and make decisions between prospects or lotteries by employing utility functions and some additional parameters given by a so called ‘comparison operator’. Agents’ comparison between lotteries involves interference effects that denote their risk perceptions from the ambiguity about prospect realisation when making a lottery selection. The above framework that builds upon the assumption of non-commuting lottery observables can have a wide class of applications to finance and asset pricing. We review here a case of an investment in two complementary risky assets about which the agent possesses non-commuting price expectations that give raise to a state dependence in her trading preferences. We summarise by discussing some other behavioural finance applications of the QP based selection behaviour framework