Asset trading under non-classical ambiguity and heterogeneous beliefs

Abstract

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.