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Rational decisions, random matrices and spin glasses


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  • Stefano Galluccio
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Marc Potters

    (Science & Finance, Capital Fund Management)


We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of "optimal" solutions is generically exponentially large: rationality is thus de facto of limited use. In addition, this problem is related to spin glasses with Lévy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.

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Bibliographic Info

Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500054.

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Date of creation: Jan 1998
Date of revision:
Publication status: Published in Physica A 259,449 (1998)
Handle: RePEc:sfi:sfiwpa:500054

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Cited by:
  1. M. Andrecut, 2013. "Spin Glasses and Nonlinear Constraints in Portfolio Optimization," Papers, 1311.2511,
  2. Jane M. Binner & Peter Tino & Jonathan Tepper & Richard G. Anderson & Barry Jones & Graham Kendall, 2009. "Does money matter in inflation forecasting?," Working Papers, Federal Reserve Bank of St. Louis 2009-030, Federal Reserve Bank of St. Louis.
  3. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 375(2), pages 584-598.
  4. Thomas Lux, 2007. "Application of Statistical Physics in Finance and Economics," Working Papers, Warwick Business School, Finance Group wp07-09, Warwick Business School, Finance Group.
  5. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers, Warwick Business School, Finance Group wpn06-07, Warwick Business School, Finance Group.
  6. Lisewski, Andreas Martin & Lichtarge, Olivier, 2010. "Untangling complex networks: Risk minimization in financial markets through accessible spin glass ground states," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 389(16), pages 3250-3253.
  7. Andreas Martin Lisewski, 2009. "Global risk minimization in financial markets," Papers, 0908.0682,
  8. Bertram, William K., 2008. "Measuring time dependent volatility and cross-sectional correlation in Australian equity returns," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 387(13), pages 3183-3191.
  9. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers, cond-mat/0402389,, revised Sep 2006.
  10. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank, European Central Bank.
  11. Matthias Raddant & Friedrich Wagner, 2013. "Phase Transition in the S&P Stock Market," Kiel Working Papers, Kiel Institute for the World Economy 1846, Kiel Institute for the World Economy.
  12. Szilard Pafka & Imre Kondor, 2001. "Evaluating the RiskMetrics Methodology in Measuring Volatility and Value-at-Risk in Financial Markets," Papers, cond-mat/0103107,
  13. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers, 1205.0877,, revised Jul 2012.
  14. Diane Wilcox & Tim Gebbie, 2004. "Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market," Papers, cond-mat/0404416,, revised Sep 2007.


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