Rational Decisions, Random Matrices and Spin Glasses

Details Rational Decisions, Random Matrices and Spin Glasses Rational Decisions, Random Matrices and Spin Glasses

1998-01-21

arxiv.org/abs/cond-mat/9801209v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

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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