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Rational decisions, random matrices and spin glasses

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Author Info
Stefano Galluccio
Jean-Philippe Bouchaud (Science & Finance, Capital Fund Management, CEA Saclay;)
Marc Potters (Science & Finance, Capital Fund Management)

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

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  1. Diane Wilcox & Tim Gebbie, 2004. "Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market," Quantitative Finance Papers cond-mat/0404416, arXiv.org, revised Sep 2007. [Downloadable!]
  2. Andreas Martin Lisewski, 2009. "Global risk minimization in financial markets," Quantitative Finance Papers 0908.0682, arXiv.org. [Downloadable!]
  3. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Quantitative Finance Papers cond-mat/0402389, arXiv.org, revised Sep 2006. [Downloadable!]
  4. Szilard Pafka & Imre Kondor, 2001. "Evaluating the RiskMetrics Methodology in Measuring Volatility and Value-at-Risk in Financial Markets," Quantitative Finance Papers cond-mat/0103107, arXiv.org. [Downloadable!]
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