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Utility maximization in incomplete markets with random endowment
被引：31
作者：
Jakša Cvitanić
Walter Schachermayer
Hui Wang
机构：
[1] Department of Mathematics,
[2] USC,undefined
[3] 1042 W 36 Pl,undefined
[4] DRB 155,undefined
[5] Los Angeles,undefined
[6] CA 90089-1113,undefined
[7] USA (e-mail: cvitanic@math.usc.edu)
,undefined
[8] Department of Statistics,undefined
[9] Probability Theory and Actuarial Mathematics,undefined
[10] Vienna University of Technology,undefined
[11] Wiedner Hauptstrasse 8-10,undefined
[12] A-1040 Wien,undefined
[13] Austria (e-mail: wschach@fam.tuwien.ac.at)
,undefined
[14] Department of Statistics,undefined
[15] Columbia University,undefined
[16] New York,undefined
[17] NY 10027,undefined
[18] USA (e-mail: wanghui@stat.columbia.edu)
,undefined
关键词：
Key words: Utility maximization, incomplete markets, random endowment, duality;
JEL Classification: G11, G12; C61;
Mathematics Subject Classification (1991): Primary 90A09, 90A10; secondary 90C26;
D O I：
10.1007/PL00013534
中图分类号：
学科分类号：
摘要：
This paper solves the following problem of mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of \documentclass[12pt]{minimal}
\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{upgreek}
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\begin{document}
$({\bf L}^\infty)^*$\end{document} (the dual space of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
${\bf L}^\infty$\end{document}).
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页码：259 / 272
页数：13
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