标题： 影子价格，分数布朗运动，以及交易成本下的投资组合优化 显示英文标题

标题： Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

摘要： 我们继续分析我们之前论文（Czichowsky/Schachermayer/Yang 2014）中关于在比例交易成本下投资组合优化时影子价格过程存在的问题。在那里，我们证明了对于满足“有限风险下无无限利润”条件$(NUPBR)$的连续价格过程$S=(S_t)_{0\leq t\leq T}$，答案是肯定的。该条件要求$S$是一个半鞅，因此对于由分数布朗运动驱动的模型来说过于严格。在本文中，我们在较弱的“双向交叉”条件$(TWC)$下得出了相同的结论，该条件不要求$S$是一个半鞅。利用 R.~Peyre 的最新结果，这使我们能够证明指数分数布朗运动和定义在正半轴上具有合理渐近弹性的效用函数$all$的影子价格存在。这类效用函数的典型例子是对数效用或幂效用。 显示英文摘要

摘要： We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive answer for a continuous price process $S=(S_t)_{0\leq t\leq T}$ satisfying the condition $(NUPBR)$ of "no unbounded profit with bounded risk". This condition requires that $S$ is a semimartingale and therefore is too restrictive for applications to models driven by fractional Brownian motion. In the present paper, we derive the same conclusion under the weaker condition $(TWC)$ of "two way crossing", which does not require $S$ to be a semimartingale. Using a recent result of R.~Peyre, this allows us to show the existence of a shadow price for exponential fractional Brownian motion and $all$ utility functions defined on the positive half-line having reasonable asymptotic elasticity. Prime examples of such utilities are logarithmic or power utility.