The pilot wave function and its uses outside of quantum mechanics Let us recall our discussion on Bohmian mechanics in Chapter 6. The idea of using Bohmian mechanics outside of quantum mechanics is not new anymore. Khrennikov [1] provides for an overview on how this model can contribute in precise terms to areas such as economics and finance.1 Historically, the work by Bohm and Hiley [2] and also Hiley and Pylkkanen [3] brought forward the idea that the pilot wave function could be seen as a wave function containing information. In Khrennikov [4], Choustova [5], and Haven [6], the idea of using pilot wave theory to finance was investigated. Khrennikov [1] (p. 160) remarks that “the force induced by the pilot wave field does not depend on the amplitude of the wave.” He cites the argument made by Bohm and Hiley [2] that because of this property the pilot wave is an information wave. The various interpretations (with applications) of the wave function will be covered in detail in Chapter 13. Here are some of the key features which can be of use in an financial/economics setting. When the wave function is not factorized, then a change in the price of a stock i will affect the prices of stocks, j , with j ≠ i . See Khrennikov [1] (p. 161). The Bohmian theory, as we remarked already in Chapters 1 and 6, is non-local.
We apply methods of quantum mechanics for mathe-matical modeling of price dynamics at financial mar-ket. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven. Our model expresses complexity of financial market: tra-ditional description of price dynamics is completed by Schrödinger’s dynamics for the pilot wave of expecta-tions of traders. This is a kind of socio-economic model for financial market
We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like
V(q) ("hard" market conditions, e.g., natural resources) and quantum-like
U(q) (behavioral market conditions). On one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W.Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W. J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).
In the so called ‘causal’ interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.
We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V ( q ) ("hard" market conditions, e.g., natural resources) and quantum-like U ( q ) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).
In this talk we intend to provide for an overview of the uses we can make in financial economics of several quantum physical concepts. We introduce and briefly discuss the so called information wave function. We discuss how the information wave function can be of use in financial option pricing. We then briefly allude on how the information wave function can be used in arbitrage. We briefly discuss how the information wave concept can be connected to measures of information. We round off the paper on recent work we are doing with Andrei Khrennikov on i) testing probability interference in psychology (Khrennikov and Haven 2006 (I)) and ii) finding uses of ‘financial ’ nonlocality and entanglement (Khrennikov and Haven 2006 (II)). In summary this talk addresses interference (probability interference), financial entanglement and looks at using the wave function in a variety of ways within an economics/finance – political science – social interaction environment.