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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)

Abstract

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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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
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Publication status: Published in Physica A 259,449 (1998)
Handle: RePEc:sfi:sfiwpa:500054

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Cited by:
  1. Diane Wilcox & Tim Gebbie, 2004. "Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market," Papers cond-mat/0404416, arXiv.org, revised Sep 2007.
  2. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers cond-mat/0402389, arXiv.org, revised Sep 2006.
  3. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank.
  4. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
  5. Matthias Raddant & Friedrich Wagner, 2013. "Phase Transition in the S&P Stock Market," Papers 1306.2508, arXiv.org.
  6. M. Andrecut, 2013. "Spin Glasses and Nonlinear Constraints in Portfolio Optimization," Papers 1311.2511, arXiv.org.
  7. Bertram, William K., 2008. "Measuring time dependent volatility and cross-sectional correlation in Australian equity returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3183-3191.
  8. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
  9. Szilard Pafka & Imre Kondor, 2001. "Evaluating the RiskMetrics Methodology in Measuring Volatility and Value-at-Risk in Financial Markets," Papers cond-mat/0103107, arXiv.org.
  10. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
  11. Andreas Martin Lisewski, 2009. "Global risk minimization in financial markets," Papers 0908.0682, arXiv.org.
  12. 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, vol. 389(16), pages 3250-3253.
  13. Binner, J.M. & Tino, P. & Tepper, J. & Anderson, R. & Jones, B. & Kendall, G., 2010. "Does money matter in inflation forecasting?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4793-4808.

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