Three-Dimensional Brownian Motion and the Golden Ratio Rule
Three-Dimensional Brownian Motion and the Golden Ratio Rule
复制标题
三维布朗运动和黄金比例规则
DOI：
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发表时间：
2013
期刊：
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通讯作者：
G. Peskir
中科院分区：
文献类型：
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作者：
K. Glover;H. Hulley;G. Peskir
设X =（Xt）t=0是（0，8）中的一个瞬态扩散过程，扩散系数s> 0，尺度函数L满足Xt？8、t？8，让它表示其运行最小值t = 0，并让？设c（i，x）=1-2L（x）/L（i），我们证明了停时使E（|? - 不|- ?)在X的所有停止时间t上（具有有限平均值），其中最优边界f* 可以被表征为对于i > 0，严格保持在曲线h（i）= L-1（L（i）/2）上方的最小解。特别地，当X是三维布朗运动的径向部分时，我们发现在哪里？=（1+v5）/2=1.61.就是黄金分割率推导出的结果适用于问题的最优交易中存在的泡沫，我们表明，黄金比例规则提供了一个严格的最优性参数的选择，众所周知的黄金回撤在技术分析的资产价格。
Let X =(Xt)t=0 be a transient diffusion processin (0,8) with the diffusion coeffcient s> 0 and the scale function L such that Xt ?8 as t ?8 ,let It denote its running minimum for t = 0, and let ? denote the time of its ultimate minimum I8 .Setting c(i,x)=1-2L(x)/L(i) we show that the stopping time minimises E(|? - t|- ?) over all stopping times t of X (with finite mean) where the optimal boundary f* can be characterised as the minimal solution to staying strictly above the curve h(i)= L-1(L(i)/2) for i > 0. In particular, when X is the radial part of three-dimensional Brownian motion, we find that where ? =(1+v5)/2=1.61 ... is the golden ratio. The derived results are applied to problems of optimal trading in the presence of bubbles where we show that the golden ratio rule offers a rigourous optimality argument for the choice of the well known golden retracement in technical analysis of asset prices.