set SECURITIES;

param K >= 0.0;               # utility parameter
param interest >= 0.0;        # riskless return on bond
param r{SECURITIES};
param sigma{i in SECURITIES};
param rho{SECURITIES,SECURITIES};
param q{i in SECURITIES, j in SECURITIES} := rho[i,j] * sigma[i] * sigma[j];

var x{SECURITIES} >= 0;   # do not allow short sales
var bond          >= 0;

minimize obj:
	0.5 * K * sum{i in SECURITIES, j in SECURITIES} q[i,j] * x[i] * 
	x[j] - sum{i in SECURITIES} r[i]*x[i] - interest * bond;
 
subject to fully_invested :
	sum{i in SECURITIES} x[i] + bond = 1.0;