Pareto efficiency and financial fairness under limited expected loss constraint
研究了在有限预期损失约束下集体资产配置的帕累托效率和金融公平性，提出了一种新的共享规则并证明其最优性，对风险控制和资产分配有指导意义。
This paper investigates the Pareto efficiency and financial fairness in a collective asset allocation under a limited expected loss (LEL) constraint. By studying a constrained collective optimization problem, we characterize a constrained version of Pareto optimality, named LEL-Pareto optimality, within the admissible class of sharing rules. We propose a novel sharing rule, referred to as the LEL sharing rule, as an alternative to widely used proportional sharing rules. We rigorously demonstrate that every LEL sharing rule is LEL-Pareto-optimal and vice versa, thereby establishing a novel Borch-like criterion in a risk-constrained setting. Under the financial fairness condition, we derive a unique LEL sharing rule through a fixed-point iteration scheme by solving a highly non-linear system of Lagrange multipliers related to LEL-constrained optimization for collective utility and the financial fairness condition. Under mild conditions, we achieve global convergence and establish the existence of a unique fixed point of the iterative algorithm. Our numerical analysis affirms the theoretical findings and underscores the positive influence of the LEL constraint among prevalent proportional sharing rules, emphasizing the importance of risk control in practical scenarios.