Stochastic Equilibria: Existence, Spanning Number, and the `No Expected Financial Gain from Trade' Hypothesis
在连续时间证券交易和消费的背景下，证明了随机均衡的存在性，并质疑了“交易有预期金融收益”假设在多商品经济中的适用性。定义了经济的跨越数，并展示了其与信息结构的关系。
Stochastic equilibria under uncertainty with continuous-time security trading and consumption are demonstrated in a general setting. A common question is whether the current price of a security is an unbiased predictor of the future price of the security plus intermediate dividends. This is the hypothesis of expected financial gains from trade. The relevance of this hypothesis in multi-good economies is called into question by the following demonstrated fact. For each set of probability assessments there exists a corresponding equilibrium, one with the original agents, original equilibrium allocations, and no expected financial gains from trade under the given probability assessments. The spanning number of the economy is defined as the fewest number of security markets required to sustain a complete markets equilibrium (in a dynamic sense made precise in the paper). The spanning number is linked directly to agent primitives, in particular the manner in which new information resolves uncertainty over time. The spanning number is shown to be invariant under bounded changes in expectations. Several examples are given in which the spanning number is finite even though the number of potential states of the world is infinite.