A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion
A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion
复制标题
与几何布朗运动的算术平均值具有相同边际的布朗片鞅
DOI：
10.1214/ejp.v14-674
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发表时间：
2009
影响因子：
1.4
通讯作者：
S. Sheu
中科院分区：
文献类型：
--
作者：
S. Sheu;S. Sheu
我们构造了一个与几何布朗运动的算术平均具有相同边缘的鞅。这简短地证明了P. Carr等人关于几何布朗运动的算术平均沿凸阶递增的最新结果。布朗表在构造中起着至关重要的作用。当布朗运动被一个稳定的从属运动所代替时，我们的方法也可以应用。
We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion.This provides a short proof of the recent result due to P. Carr et al that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion is replaced by a stable subordinator.