Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales
在无限维索伯列夫空间（包括希尔伯特空间）中建立竞争均衡的存在性与最优性，允许无下界的消费集和无限资产的无限制卖空，并给出基于禀赋和偏好的无套利条件。
Following Chichilnisky and Chichilnisky-Kalman we establish existence and optimality of competitive equilibrium when commodity spaces are infinite dimensional Sobolov spaces, including Hilbert spaces such as weighted L2 which have L∞, as dense subspaces. We allow general consumption sets with or without lower bounds, thus including securities markets with infinitely many assets and unbounded short sales, and economies with production. We give non-arbitrage conditions on endowments and preferences which suffice for the existence of an equilibrium. Prices are in the same space as commodities. Equilibrium allocations are approximated by allocations in other frequently used spaces such as C(R) and L∞.