仅有风险资产的市场存在非负均衡价格的充要条件

Necessary and Sufficient Condition for the Existence of a Nonnegative Equilibrium Price in Market with Risk Assets

对满足通常假设条件的、仅含有风险资产的均值 方差资本市场 ,给出了可使市场中每种资产的总需求与总供给相等的非负均衡价格向量存在惟一的充要条件 ,即第i个投资者所要求最优期望收益率 .开始时 ,他所持有第 j种资产的分数与相对于市场的一般均值 方差模型最优解的第 j个分量三者的乘积 ,再对不同的i、j求和以后应等于 1.导出了均衡价格的计算公式 ,公式表明 ,第 j种资产的均衡价格等于各个投资者初始投入资产总值之和除以第j种资产的总量 ,再乘以市场证券组合的第

Under usual assumptions, derived is a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balance in the meanvariance(MV) capital market with risk assets. The condition requires that the sum of the products of the optimal expected rate of return for the i th investor, the fraction of security j held by this investor and the j th component of the optimal solution of the generic market MV model, with respect to different i and j , should be 1. An explicit formula for the equilibrium price is obtained, which shows that the equilibrium price for asset j is equal to the product of the j th component of the market portfolio and the sum of different investors′ initial endowments, divided by the total quantity of asset j .