分数布朗运动与二元市场模型

Fractional brownian motion and binary market models

证明了对于Hurst指数大于二分之一情形的分数布朗运动的Donsker型逼近定理,使用这种逼近,构造了一个弱收敛于Black-Scholes模型的分数模拟的初级市场模型,得到在此模型中存在着套利机会。

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case of the Hurst index greater than one half. With this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black Scholes model. We show that there exist arbitrage opportunities in this model.