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Rational Decisions, Random Matrices and Spin Glasses

Author

Listed:
  • Stefano Galluccio

    (CEA-Saclay and Science et Finance)

  • Jean-Philippe Bouchaud

    (CEA-Saclay and Science et Finance)

  • Marc Potters

    (CEA-Saclay and Science et Finance)

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 L\'evy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.

Suggested Citation

  • Stefano Galluccio & Jean-Philippe Bouchaud & Marc Potters, 1998. "Rational Decisions, Random Matrices and Spin Glasses," Papers cond-mat/9801209, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/9801209
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    Cited by:

    1. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    2. Sharkasi, Adel & Crane, Martin & Ruskin, Heather J. & Matos, Jose A., 2006. "The reaction of stock markets to crashes and events: A comparison study between emerging and mature markets using wavelet transforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 511-521.
    3. Thomas Lux, 2006. "Applications of Statistical Physics in Finance and Economics," Working Papers wpn06-07, Warwick Business School, Finance Group.
    4. 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.
    5. Pafka, Szilárd & Kondor, Imre, 2001. "Evaluating the RiskMetrics methodology in measuring volatility and Value-at-Risk in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 305-310.
    6. M. Andrecut, 2013. "Spin Glasses and Nonlinear Constraints in Portfolio Optimization," Papers 1311.2511, arXiv.org.
    7. Andreas Martin Lisewski, 2009. "Global risk minimization in financial markets," Papers 0908.0682, arXiv.org.
    8. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.
    9. 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.
    10. Imre Kondor & István Csabai & Gábor Papp & Enys Mones & Gábor Czimbalmos & Máté Sándor, 2014. "Strong random correlations in networks of heterogeneous agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 203-232, October.
    11. Matthias Raddant & Friedrich Wagner, 2016. "Phase transition in the S&P stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 229-246, October.
    12. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers cond-mat/0402389, arXiv.org, revised Sep 2006.
    13. 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.
    14. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
    15. 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.
    16. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 294-298.
    17. Gili Rosenberg & Poya Haghnegahdar & Phil Goddard & Peter Carr & Kesheng Wu & Marcos L'opez de Prado, 2015. "Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer," Papers 1508.06182, arXiv.org, revised Aug 2016.
    18. 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.
    19. 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.
    20. Gao, Yan & Gao, Yao, 2015. "Statistical properties of short-selling and margin-trading activities and their impacts on returns in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 293-307.
    21. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.

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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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