摘要翻译:
本文研究了两个布朗运动的经典镜像耦合和同步耦合是否分别使对应的几何布朗运动的耦合时间最小化和最大化的问题。我们在任意有限时间范围内建立了两个耦合的最优性的刻画,并证明了与布朗运动不同的是,即使几何布朗运动是鞅,最优性在一般情况下也是失败的。另一方面,我们证明了在遍历平均和无限时域条件下,对于一般的(可能是非鞅的)几何布朗运动,镜像耦合和同步耦合总是最优的。我们证明了这两个耦合是有效的当且仅当它们在有限时间范围内是最优的,并给出了次优时有效耦合的猜想答案。
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英文标题:
《Mirror and Synchronous Couplings of Geometric Brownian Motions》
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作者:
Saul D. Jacka, Aleksandar Mijatovic, and Dejan Siraj
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最新提交年份:
2013
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分类信息:
一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Quantitative Finance 数量金融学
二级分类:Portfolio Management 项目组合管理
分类描述:Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要:
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.
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PDF链接:
https://arxiv.org/pdf/1304.1999