资产定价第一基本定理的拓扑描述

THE TOPOLOGICAL CHARACTERIZATION ABOUT FIRST FUNDAMENTAL THEOREM OFASSET PRICING

资产定价的第一基本定理是数量金融学中核心的定理之一 ,本文证明了在 L∞ 的弱 * 拓扑 σ(L∞ ,L1)中的凸集分离定理 ,并在此定理的基础上给出了没有无风险免费午餐的拓扑描述 ,证明了市场公平性与没有无风险免费午餐条件的等价性 ,从而重新证明了资产定价的第一基本定理 .

The first findamental theorem of asset pricing is a core in mathematical finance. In the paper the separate theorem of convex set with weak topology σ(L ∞,L 1) is proved, and the topological characterization about No Free Lunch with Vanishing Risk(NFLVR) Condition is given, from it, the equivalency between exist of equivalent martingale measures and NFLVR is proved, this is the first fundamental theorem of asset pricing.