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Rational Decisions, Random Matrices and Spin Glasses

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  • 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.

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Paper provided by arXiv.org in its series Papers with number cond-mat/9801209.

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Date of creation: Jan 1998
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Handle: RePEc:arx:papers:cond-mat/9801209

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Web page: http://arxiv.org/

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Cited by:
  1. Andreas Martin Lisewski, 2009. "Global risk minimization in financial markets," Papers 0908.0682, arXiv.org.
  2. 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.
  3. 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.
  4. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank.
  5. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers cond-mat/0402389, arXiv.org, revised Sep 2006.
  6. 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.

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