关于资产定价的第一基本定理

ON THE FIRST FUNDAMENTAL THEOREM OF ASSET PRICING

资产定价的第一基本定理是数理金融学中最核心的定理之一 ,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 fundamental theorem of asset pricing is the one of the most important of mathematical finance.This paper proofs the convex set separation theorem at weak * topology σ(L ∞,L 1) of L ∞. And on the base of the theorem,the author gives the topology description of no free lunch with vanishing risk;and proofs the equivalence between the viability of market and no free lunch with vanishing risk condition,so anew proofs the first fundamental theorem of asset pricing.