RATIONAL DECISIONS, RANDOM MATRICES AND SPIN-GLASSES

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and ra ndom matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each of them is fragile: rationality is in this case of lim ited use. In addition, this problem is related to spin glasses with Le vy-like (long-ranged) couplings, for which we show that the ground sta te is not exponentially degenerate. (C) 1998 Published by Elsevier Sci ence B.V. All rights reserved.