探讨具有有限多个风险资产和一个无风险资产、有多个投资者参与的资本资产市场中非负均衡价格的存在性条件与确定问题, 从以下角度改进了现有结果：采用期望损失(Expectedshortfall, 简称~ES)作为风险度量, 保证了均值-~ES~框架下所得结果与期望效用极大化原理结果的一致性; 对证券收益的联合分布不做假设; 考虑了比例交易费用对价格的影响, 所得结果更贴近现实的金融市场; 不仅给出了非负均衡价格存在唯一的充要条件, 而且导出了其具体表达式; 在对比分析其与现有结果异同的同时, 还讨论了所给充要条件与定价公式的应用与经济解释.

For the asset market with several risky assets and one riskless asset and finite numbers of investors,   the existence   and determination of the nonnegative
equilibrium price vector are investigated. The results improve current results from the following aspects: By adopting the expected shortfall (ES) as
the risk measure, the results obtained under the mean-ES framework is consistent with those derived under the expected utility maximization; it is not necessary  to impose any assumption on the joint distribution of securities' returns; by considering the affect of proportional transaction costs on equilibrium prices, the results are more suitable for real financial markets; the authors not only derive a necessary and sufficient condition for the existence and
uniqueness of nonnegative equilibrium prices that clears the asset market, but also give an explicit formula for the equilibrium price vector; except for comparing the conclusions with existing results, the authors also discuss the application and economic implication of the given condition and formula.