Abstract
Stock exchanges are modeled as nonlinear closed-loop systems where the plant dynamics is defined by known stock market regulations and the actions of agents are based on their beliefs and behavior. The decision of the agents may contain a random element, thus we get a nonlinear stochastic feedback system. The market is in equilibrium when the actions of the agents reinforce their beliefs on the price dynamics. Assuming that linear predictors are used for prediction of the price process, a stochastic approximation procedure for finding market equilibrium is described. The proposed procedure is analyzed using the theory of Benveniste et al. (Adaptive algorithms and stochastic approximations. Springer, Berlin, 1990). A simulation result is also presented.
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References
Andrieu C, Moulines É, Priouret P (2005) Stability of stochastic approximation under verifiable conditions. SIAM J Control Optim 44:283–312
Benveniste A, Métivier M, Priouret P (1990) Adaptive algorithms and stochastic approximations. Springer, Berlin
Delyon B (1996) General results on the convergence of stochastic algorithms. IEEE Trans Autom Control 41:1245–1256
Gerencsér L (1992) Rate of convergence of recursive estimators. SIAM J Control Optim 30:1200–1227
Gerencsér L, Mátyás Z (2005) Almost sure convergence of stochastic approximation algorithms with resetting. MTA SZTAKI, working paper
Greenfinch P (2001) Behavioral finance definitions. http://www.perso.wanadoo.fr/pgreenfinch/bfdef.htm
Glosten LR, Milgrom PR (1985) Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. J Financ Econ 14:71–100
Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47:263–292
Kostolany A (1991) Börsenpsychologie. ECON Verlag GmbH, New York
LeBaron B (2002) Building the Santa Fe artificial stock market. Brandeis University, working paper
Ljung L, Söderström T (1983) Theory and practice of recursive identification. The MIT Press
Lucas RE, Sargent T (eds.) (1981) Rational expectations and econometric practice. University of Minnesota Press, Minneapolis
O’Hara M (2000) Market microstructure theory. Blackwell Publishers, Oxford
Sallans B, Pfister A, Karatzoglou A, Dorffner G (2003) Simulation and validation of an integrated markets model. J Artif Soc Soc Simul 6
Shefrin H (2001) Behavioral corporate finance. Leavey School of Business, working paper, http://www. business.scu.edu/faculty//research/working_papers/workingpapers02.htm#0211WP
Simon HA (1979) Rational decision making in business organizations. Am Econ Rev 4:493–513
Willems JC (1997) On interconnections, control and feedback. IEEE Trans Autom Control 42:326–339
Zames G (1966) On the input-output stability of time-varying nonlinear feedback systems, Part II: conditions involving circles in the frequency plane and sector nonlinearities. IEEE Trans Autom Control 11:465–476
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Gerencsér, L., Mátyás, Z. A behavioral stock market model. Math Meth Oper Res 67, 43–63 (2008). https://doi.org/10.1007/s00186-007-0164-y
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DOI: https://doi.org/10.1007/s00186-007-0164-y