DUALITY THEORY FOR PORTFOLIO OPTIMISATION UNDER TRANSACTION COSTS

被引：28

作者：

Czichowsky, Christoph ^{[1
]}

Schachermayer, Walter ^{[2
]}

机构：

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

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

来源：

ANNALS OF APPLIED PROBABILITY | 2016年 / 26卷 / 03期

基金：

瑞士国家科学基金会; 欧洲研究理事会; 奥地利科学基金会;

关键词：

Utility maximisation; proportional transaction costs; convex duality; shadow prices; supermartingale deflators; optional strong supermartingales; predictable strong supermartingales; logarithmic utility; TRADING STRATEGIES; OPTIMAL INVESTMENT; MARKET; SELECTION; ARBITRAGE;

D O I：

10.1214/15-AAP1136

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the problem of portfolio optimisation with general cadlag price processes in the presence of proportional transaction costs. In this context, we develop a general duality theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a "sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form.

引用

页码：1888 / 1941

页数：54

共 18 条

[1] MARTINGALES AND ARBITRAGE IN SECURITIES MARKETS WITH TRANSACTION COSTS [J].