Endogenous Completeness of Diffusion Driven Equilibrium Markets
研究连续时间异质代理人经济中市场内生完备的均衡存在性，发现若价格是时间和状态变量的实解析函数，则股息波动非退化足以保证市场完备，并给出两种基准情形的易用条件。
We study the existence of equilibria with endogenously complete mar- kets in a continuous-time, heterogenous agents economy driven by a multi- dimensional diï¬usion process. Our main results show that if prices are real analytic as functions of time and the state variables of the model then a suï¬- cient condition for market completeness is that the volatility of dividends be nondegenerate. In contrast to previous research, our formulation does not require that securities pay terminal dividends and thus allows for both ï¬nite or inï¬nite horizon economies. We illustrate our results by providing easily applicable conditions for market completeness in two benchmark cases: that where the state variables are given by a vector autoregressive process and that where they are given by a vector of autonomous diï¬usion processes. We also provide counterexamples which show that real analyticity cannot be dispensed with if one is to deduce dynamic market completeness from the structure of dividends.