Non-Negative Equilibrium Prices and Market Portfolio Under Minimax Diversification with Non-Homogeneous Investors

Market equilibrium is characterized by a state wherein aggregate demand equals aggregate supply for all assets, a condition arising from consumers maximizing utility within budget constraints and producers maximizing profits. This paper investigates a financial market populated by non-homogeneous investors who may employ heterogeneous deviation measures to formulate their risk functions. By integrating the minimax risk diversification principle with the framework of individual utility maximization, we analytically derive the master fund for each investor. Furthermore, we establish the necessary and sufficient conditions for the existence of a unique non-negative equilibrium price system for risky assets and provide its explicit formula. A key finding is that the market portfolio is a convex combination of all investors’ master funds.