A note on a minimax rule for portfolio selection and equilibrium price system

This paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction. A numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm. For the problem without short sale restriction, we derive a analytical expression for the optimal solution, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system, and an explicit formula for the price system. Furthermore, a numerical example is given to show the validity of the method.