Modelling agents’ asset price expectations: a quantum theoretical paradigm.

Nowadays, human decision making in economic and finance decisions  is facing increasing complexity due to a) non- classical assessment of probabilities associated with states of the world and  outcomes (cf.  seminal works by Kahneman and Tversky (1979) and Prelec (1998)), b)  non Bayesian updating of information and finally, the most difficult, albeit existent  situation – the inability to assess the state space of all  the outcomes and hence their probabilities . 

Situations, where no well-founded subjective probabilities can be devised, known as ambiguity could be well captured through probabilistic models of quantum mechanics (also known as ‘ Quantum-Like’ models)   by usage of complex- probability amplitudes that correspond to ambiguity in respect to the exact probabilistic  distribution on the values of a random variable ( e.g. the distribution of  price states of a financial asset). 

In the context of finance market, as presented in Khrennikova (2016), agents’ ambiguity on the future distribution of assets’ prices and the corresponding returns can be manifest in  the impossibility to form a classical probabilistic distribution (normal distribution of returns is  the foundation of Markowitz Modern Portfolio Theory)  for the returns of financial assets. E.g., as highlighted in Shiller (2003), agents expectations on future asset price are often based on erogenous expectations and yield excess volatility on  the stock market.

We  propose a model based on quantum probabilistic framework,  where the price dynamics  of some financial assets is created by the  informational bath that consists of the agents expectation about future asset prices (Khrennikova, 2016). 

One of the basic behavioural factors leading to quantum-like dynamics of forecasted prices is  the irrationality of expectations of the agents on the financial market. It leads to a deeper type of uncertainty than given by classical probability theory, e.g., in the framework of the classical financial mathematics, based on theory of stochastic processes.

The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-state superposition and entanglement of different financial assets.

The long-term equilibrium state in asset price dynamics can be well captured with the aid of  a quantum master equation that has been successfully applied to decision making problems under uncertainty, e.g. Asano et al (2010), Khrennikova et al (2014). 

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