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National Conference on Artificial Intelligence

A Survey of Possible Uses of Quantum Mechanical Concepts in Financial Economics.

Emmanuel E. Haven

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

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.

Related papers

Elementary Quantum Mechanical Principles and Social Science: Is There a Connection?

Emmanuel E. Haven

In this paper we provide first for a brief overview of some of the work which has been performed on the interface of quantum mechanics and macroscopic systems (such as economics). We then provide for an overview of how such quantum mechanical concepts can enter financial option pricing theory. We round off the paper with some suggestions on where this area of research can be heading in the near future.

Romanian Journal of Economic Forecasting•Jan 1, 2008•7 citations

Other applications to economic/financial theory

Emmanuel E. Haven, Andrei Yu. Khrennikov

This chapter attempts to delve deeper into the question on how quantum mechanical techniques can be brought closer into the realm of economics and finance. The (non-)Hermiticity of finance-based operators? Hermiticity of operators was discussed in Chapter 4 of the book. We again take up this very important concept in the context of financial asset pricing. It is a classical result from quantum mechanics that the existence of Hermiticity of the Hamiltonian operator is intimately linked with the notion of conservation of probability. The existence of Hermiticity is also known to be closely linked to the concept of spatial localization. Please see below. Baaquie [1] makes the important argument that the Black-Scholes Hamiltonian is non-Hermitian and this condition provides for the need to satisfy the martingale condition. Please recall that the martingale property was covered in Chapter 2, Section 2.9. It is also important to mention that Luigi Accardi has indicated that it is white noise which may be the cause of non-Hermiticity in a finance context. One can argue that within an economics/finance context, the equivalent of the state function, using Baaquie [1] [2], can be the option price function. A similar interpretation can also be found in the paper by Li and Zhang [3] (see also Haven [4]). Please note that the work of Li and Zhang is covered in Section 13.12 of this chapter.

Cambridge University Press eBooks•Jan 17, 2013•0 citations

Financial/economic theory in crisis

Emmanuel E. Haven, Andrei Yu. Khrennikov

In this chapter and Chapters 11, 12, and 13, we will discuss quantum-like models with financial applications in mind. The very last chapter of this book will analyze the sources of quantum-like processing in the brain. The concept of non-arbitrage, as we have indicated before (see Section 4.18.3) is of key importance in financial models. We reiterate its importance in this chapter. We also briefly mention a popular finance model. In the coming chapters, the wave function will sometimes have an information interpretation. Therefore we also discuss the informational aspects of the classical financial theory (see Section 10.1). This chapter is meant to introduce the reader to some of the key achievements in financial theory. By doing so, we hope to convince the reader, in later chapters, that some of those very achievements can possibly be reformulated with the help of the wave function approach. Section 10.3 in this chapter will give a flavor of how Fourier integration can possibly be used to model George Soros' concept of reflexivity. Relevance of the concepts of efficiency and non-arbitrage: a brief discussion With the 2008 financial crisis, the concept of efficiency may have been seriously questioned. Indeed the financial market in September 2008 did take a tremendous hit and the ensuing price movements would not be consistent with a so-called efficient market.

Cambridge University Press eBooks•Jan 17, 2013•0 citations

Bohmian mechanics in finance and economics

Emmanuel E. Haven, Andrei Yu. Khrennikov

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.

Cambridge University Press eBooks•Jan 17, 2013•0 citations

The Use of the Information Wave Function in a Drift Dependent Option Price: A Simple Example

Emmanuel E. Haven, Luigi Accardi, Guillaume Adenier +5 more

This paper briefly describes how a drift‐dependent option price is obtained, following the work of Tan [12]. We briefly argue how the information wave function concept, which has now been used in various financial settings, can be used in this type of option price.

AIP conference proceedings•Jan 1, 2009•0 citations

Other Quantum-like Models in Finance

Vikram Athalye, Emmanuel Haven

This chapter starts with the idea of a quantized version of supply and demand. We also provide for a discussion why quantum probability is useful in both option pricing and investment choice decisions. We also discuss briefly quantum-like Bayesian networks within the setting of missing financial data. We also hint toward the usefulness of open systems in social science and then dive into the very important observation that Black–Scholes Hamiltonians are non-Hermitian. Toward the end of the chapter, we give an overview of models (with and without memory and (a)symmetry between past and future times). We give some examples and then conclude the chapter with thoughts on the limitations of mathematical modelling.

Cambridge University Press eBooks•Dec 19, 2025•0 citations
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.
This chapter attempts to delve deeper into the question on how quantum mechanical techniques can be brought closer into the realm of economics and finance. The (non-)Hermiticity of finance-based operators? Hermiticity of operators was discussed in Chapter 4 of the book. We again take up this very important concept in the context of financial asset pricing. It is a classical result from quantum mechanics that the existence of Hermiticity of the Hamiltonian operator is intimately linked with the notion of conservation of probability. The existence of Hermiticity is also known to be closely linked to the concept of spatial localization. Please see below. Baaquie [1] makes the important argument that the Black-Scholes Hamiltonian is non-Hermitian and this condition provides for the need to satisfy the martingale condition. Please recall that the martingale property was covered in Chapter 2, Section 2.9. It is also important to mention that Luigi Accardi has indicated that it is white noise which may be the cause of non-Hermiticity in a finance context. One can argue that within an economics/finance context, the equivalent of the state function, using Baaquie [1] [2], can be the option price function. A similar interpretation can also be found in the paper by Li and Zhang [3] (see also Haven [4]). Please note that the work of Li and Zhang is covered in Section 13.12 of this chapter.
In this chapter and Chapters 11, 12, and 13, we will discuss quantum-like models with financial applications in mind. The very last chapter of this book will analyze the sources of quantum-like processing in the brain. The concept of non-arbitrage, as we have indicated before (see Section 4.18.3) is of key importance in financial models. We reiterate its importance in this chapter. We also briefly mention a popular finance model. In the coming chapters, the wave function will sometimes have an information interpretation. Therefore we also discuss the informational aspects of the classical financial theory (see Section 10.1). This chapter is meant to introduce the reader to some of the key achievements in financial theory. By doing so, we hope to convince the reader, in later chapters, that some of those very achievements can possibly be reformulated with the help of the wave function approach. Section 10.3 in this chapter will give a flavor of how Fourier integration can possibly be used to model George Soros' concept of reflexivity. Relevance of the concepts of efficiency and non-arbitrage: a brief discussion With the 2008 financial crisis, the concept of efficiency may have been seriously questioned. Indeed the financial market in September 2008 did take a tremendous hit and the ensuing price movements would not be consistent with a so-called efficient market.
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.
This chapter starts with the idea of a quantized version of supply and demand. We also provide for a discussion why quantum probability is useful in both option pricing and investment choice decisions. We also discuss briefly quantum-like Bayesian networks within the setting of missing financial data. We also hint toward the usefulness of open systems in social science and then dive into the very important observation that Black–Scholes Hamiltonians are non-Hermitian. Toward the end of the chapter, we give an overview of models (with and without memory and (a)symmetry between past and future times). We give some examples and then conclude the chapter with thoughts on the limitations of mathematical modelling.