ssrn-id982086 - April 23, 2007 An Evolutionary Quantum Game...

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Electronic copy of this paper is available at: http://ssrn.com/abstract=982086 April 23, 2007 An Evolutionary Quantum Game Model of Financial Market Dynamics Theory and Evidence Carlos Pedro Gonçalves Carlos Gonçalves Abstract The application of mathematical physics to economics has seen a recent de- velopment in the form of quantum game theory. Quantum game theory has become an important eld of research in multidisciplinary applications of math- ematical physics to the study of economic phenomena. We address the empirical ndings of multifractality and turbulence in nan- cial markets’ dynamics, from the point of view of evolutionary quantum game theory, proposing a quantum game theoretical model of a nancial market, that extends the behavioral framework proposed by Sornette and Zhou for the self- ful lling Ising model of the markets. The quantum market model works with a bosonic framework for evolutionary quantum game theory introduced here and is based on recent ndings within neuroeconomics and the neurobiology of decision. The model is tested against actual market data, where it is shown that it is able to reproduce some of the main multifractal signatures present in actual markets. Keywords: Bosonic Evolutionary Quantum Game Theory, Multifractals, Market Turbulence, Econophysics . JEL Classification: C73, G10, G14, G32, D83, D84, D87 Researcher at UNIDE ISCTE Business School, quantitative methods’ research line. e-mail: cpdsg@iscte.pt, carlospedrogoncalves@yahoo.com ISCTE Business School, Department of Finance. e-mail: carlos.goncalves@iscte.pt 1
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Electronic copy of this paper is available at: http://ssrn.com/abstract=982086 Acknowledgement s: We thank Professor Didier Sornette for the important discussions regarding the previous arti cial nancial market, which much con- tributed with elements for the current work. We also thank Maria Odete Gonçalves for the important discussions regarding cognitive science, neurobiology and phi- losophy, which contributed, a great deal, for the behavioral foundations of the current model. We would also like to thank the Netlogo user community and the Netlogo team at Northwestern University, for the important support in agent- based modelling. 2
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I. Introduction Ever since the identi cation of multifractal behavior in the nancial mar- kets’ price uctuations (Mandelbrot, 1999; Mandelbrot, et al. , 1997; Calvet and Fisher, 2002; Muzy et al. , 2001), an empirical fact, unexplained within standard nancial theory, there has been a search for models that provide an explanation of this phenomenon. The major problem with nancial stochastic modelling approaches such as the multifractal model of assets’ returns (MMAR) (Calvet and Fisher, 2002) and the multifractal random walk (MRW) (Muzy et al. , 2001), is that multifractal behavior is introduced through a multiplicative cascade, without a fundamen- tal theoretical grounding on agents’ behavior. Such a modelling approach is useful in terms of the immediate end result, which is the reproduction of the
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This note was uploaded on 10/24/2011 for the course SCIENCE PHY 453 taught by Professor Barnard during the Winter '11 term at BYU.

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ssrn-id982086 - April 23, 2007 An Evolutionary Quantum Game...

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