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

被引：12

作者：

Czichowsky, Christoph ^{[1
]}

Peyre, Remi ^{[2
,3
]}

Schachermayer, Walter ^{[2
,4
]}

Yang, Junjian ^{[5
]}

机构：

[1] London Sch Econ & Polit Sci, Dept Math, Columbia House,Houghton St, London WC2A 2AE, England

[2] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS, Campus Aiguillettes,BP 70239, F-54506 Vandoeuvre Les Nancy, France

[4] Swiss Fed Inst Technol, Inst Theoret Studies, Zurich, Switzerland

[5] Ecole Polytech, Ctr Math Appl CMAP, Route Saclay, F-91128 Palaiseau, France

来源：

FINANCE AND STOCHASTICS | 2018年 / 22卷 / 01期

基金：

奥地利科学基金会;

关键词：

Proportional transaction costs; Fractional Brownian motion; Shadow prices; Two-way crossing; Logarithmic utility; UTILITY MAXIMIZATION; INCOMPLETE MARKETS; OPTIMAL INVESTMENT; SEMIMARTINGALE PROPERTY; DUALITY; CONSUMPTION; ARBITRAGE; THEOREM; TIME;

D O I：

10.1007/s00780-017-0351-5

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

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.

引用

页码：161 / 180

页数：20

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