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

被引：0
作者：
Christoph Czichowsky
Rémi Peyre
Walter Schachermayer
Junjian Yang
机构：
[1] London School of Economics and Political Science,Department of Mathematics
[2] Columbia House,Fakultät für Mathematik
[3] Universität Wien,Institut Élie Cartan de Lorraine
[4] CNRS – Université de Lorraine,Institute for Theoretical Studies
[5] ETH Zürich,Centre de Mathématiques Appliquées (CMAP)
[6] École Polytechnique,undefined
来源：
Finance and Stochastics | 2018年 / 22卷
关键词：
Proportional transaction costs; Fractional Brownian motion; Shadow prices; Two-way crossing; Logarithmic utility; 91G10; 93E20; 60G48; G11; C61;
D O I：
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中图分类号：
学科分类号：
摘要：
The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes), and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market.
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页码：161 / 180
页数：19
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