Risk sharing theory advances. A new mathematical framework generalizes how risk is distributed across large markets with heterogeneous agents. Researcher Vasily Melnikov's work extends classical models to continuous agent populations, applying entropic and expected shortfall risk measures. The theory provides dual representations for value functions and characterizes acceptance sets through advanced mathematical techniques. These developments have direct implications for understanding Pareto efficiency in large financial markets and could reshape how financial institutions model portfolio optimization and systemic risk. The framework bridges quantitative finance with theoretical economics, offering practical applications for derivative pricing and risk management strategies in modern markets.