Rational Decisions, Random Matrices and Spin Glasses

15 January 1998

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

Authors

Stefano Galluccio , Marc Potters , Jean-Philippe Bouchaud