Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets
证明在连续时间证券市场中，当证券数量比独立不确定性来源多至少一个时，均衡存在且候选均衡价格过程是动态完全的，结果依赖于布朗滤波信息结构和终端股息非退化条件。
We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and from a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy. Copyright Copyright 2008 by The Econometric Society.