EQUILIBRIUM IN LINEAR CAPITAL MARKET NETWORKS

IT IS SHOWN HOW CERTAIN IDEAS IN THE SO CALLED DECOMPOSITION THEORY OF MATHEMATICAL PROGRAMMING CAN BE EXPLOITED FOR THE COMPUTATION OF EQUILIBRIUM IN A SYSTEM OF LINEAR CAPITAL MARKETS. A NETWORK REPRESENTATION OF THE INTERCONNECTION OF CAPITAL MARKETS IS GIVEN WHERE THE HOLDING OF EACH ASSET IS CONCEIVED OF AS A DIRECTED LINK. TWO TYPES OF NODES ARE DISTINGUISHED, PORTFOLIO AND MARKET, AND CONDITIONS AND CONSTRAINTS POSTULATED FOR EACH. THE FUNDAMENTAL HYPOTHESIS UNDERLYING THE GIVEN MODEL IS THAT THE FREE MARKET OPERATIONS WILL MINIMIZE THE INTERVENTIONS OF THOSE ARBITRATORS OR DEALERS WHO TAKE POSITIONS ON THEIR OWN ACCOUNTS. THE FINAL RETURN COEFFICIENTS ARE DERIVED AS THOSE MINIMIZING THOSE INTERVENTIONS. AN ALGORITHM IS AVAILABLE WHICH EFFECTIVELY CALCULATES THE FINAL VECTOR OF RETURN COEFFICIENTS. DIAGRAMS. REFERENCES.