Bubbles and Charges
用测度论形式化定义资产价格中的基本面和泡沫成分，证明在完全市场、有限代理人的一般均衡模型中，即使没有不确定性也能出现理性泡沫，为理解泡沫成因提供新视角。
The definitions of and that are standard in macroeconomics and finance are given formal representations as the countably additive part and the purely finitely additive part (a measure and a pure charge, respectively) of the supporting price system, when the commodity space is LX'. Examples illustrate that rational bubbles can occur in standard general equilibrium models with complete markets and a finite number of agents, even in the absence of uncertainty. Consider an economy which includes securities or capital goods which are claims to cash flows over (countably) infinite time, and also includes markets for all goods. Conduct the following thought experiment: for each security add the present value of the first n elements of the cash flow, and take the limit as n gets large. This limit represents the value of the security. The difference, if any, between the price of the security and its value is termed a speculative bubble. This use of the terms fundamental and is, we believe, one of those that are generally accepted. Blanchard and Fischer (1989, pp. 218-221), for example, used the terms precisely in this way. Yet confusion persists about what factors generate bubbles. Fads and irrationality have always figured prominently, and the hypothesis that these factors are important has gained some empirical support from the literature on asset price volatility. Another bubbleproducing factor is the structure of information in the market. In a partialequilibrium setting, Allen and Gorton (1988) showed that rational bubbles can exist with a finite number of agents who have asymmetric information. Although fads and asymmetric information can undeniably produce bubbles, here we focus exclusively on the phenomenon of speculative bubbles in general equilibrium models with optimizing agents, rational expectations and symmetric information. An important source of confusion, we believe, is that the term fundamental is used in connection with sunspot equilibria as well as bubble equilibria: a sunspot equilibrium is one in which prices and allocations depend on irrelevant sunspots as well as exogenous variations in fundamentals (preferences, technology and endowments). Bubbles, on this usage, reflect the effect of extrinsic uncertainty on equilibrium prices and allocations. This use of the term fundamental in connec