The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets
分析不完全金融市场中竞争均衡的结构，证明市场不完全性会导致配置的n维不确定性，即均衡分配集包含一个光滑的n维子流形。
This paper presents an analysis of the structure of competitive equilibrium in a model whose principal feature is incomplete financial markets formulated in the spirit of Arrow. Specifically, the overall payoffs or returns from financial instruments are assumed to be fixed or predetermined, independently of the operation of the economy, and these instruments are assumed to be fewer in number than required to span all potential spot markets for commodities. Our main result establishes that market incompleteness generates a corresponding degree of allocation indeterminateness: Suppose there are N + 1 spot markets, but only 0< M < N (linearly independent) financial instruments, so that the deficiency in financial markets is 0 < n = N - M < N. Then, subject to some relatively innocuous technical qualifications, the set of equilibrium allocations contains a smooth, n-dimensional submanifold. We also indicate how real indeterminacy may increase when returns (for example, the market price and promised interest on an ordinary bond) are treated as variables rather than parameters.