Arbitrage and utility maximization in market models with an insider

被引:0
作者
Huy N. Chau
Wolfgang J. Runggaldier
Peter Tankov
机构
[1] Hungarian Academy of Sciences,Alfréd Rényi Institute of Mathematics
[2] University of Padua,Department of Mathematics
[3] CREST-ENSAE Paris Tech,undefined
来源
Mathematics and Financial Economics | 2018年 / 12卷
关键词
Initial enlargement of filtration; Optimal arbitrage; No unbounded profits with bounded risk; Incomplete markets; Hedging; Utility maximization; G14;
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摘要
We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an FT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {F}_T$$\end{document}-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.
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页码:589 / 614
页数:25
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