Martingale representation theorems for initially enlarged filtrations

被引：55

作者：

Amendinger, J ^{[1
]}

机构：

[1] HypoVereinsbank AG, Int Markets, Structured Prod, D-81925 Munich, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 89卷 / 01期

关键词：

initial enlargement of filtrations; martingale preserving measure; martingale representation; utility maximization; insider trading;

D O I：

10.1016/S0304-4149(00)00015-6

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：

In this paper we transfer martingale representation theorems from some given filtration F to an initially enlarged filtration G = FV sigma(G), where G is a random variable satisfying an equivalence assumption. We use then one of these theorems to solve the problem of maximizing the expected utility from both consumption and terminal wealth for an agent having the information flow G at his disposal. (C) 2000 Elsevier Science B.V. All rights reserved. MSC. Primary 60G44; 60H05; 90A09; secondary 60H30; 90A35; 90A43.

引用

页码：101 / 116

页数：16

共 19 条

[1] Additional logarithmic utility of an insider [J].

Amendinger, J ;

Imkeller, P ;

Schweizer, M .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 75 (02) :263-286

[2]

[Anonymous], 1995, INTEGRATION PROBABIL

[3]

[Anonymous], 1990, ADV LECT MATH

[4] EXISTENCE OF OPTIMAL STRATEGIES BASED ON SPECIFIED INFORMATION, FOR A CLASS OF STOCHASTIC DECISION PROBLEMS [J].

BENES, VE .

SIAM JOURNAL ON CONTROL, 1970, 8 (02) :179-&

[5] CHANGES OF FILTRATIONS AND OF PROBABILITY MEASURES [J].

BREMAUD, P ;

YOR, M .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1978, 45 (04) :269-295

[6] OPTIMAL CONSUMPTION AND PORTFOLIO POLICIES WHEN ASSET PRICES FOLLOW A DIFFUSION PROCESS [J].

COX, JC ;

HUANG, CF .

JOURNAL OF ECONOMIC THEORY, 1989, 49 (01) :33-83

[7] THE EXISTENCE OF ABSOLUTELY CONTINUOUS LOCAL MARTINGALE MEASURES [J].

Delbaen, Freddy ;

Schachermayer, Walter .

ANNALS OF APPLIED PROBABILITY, 1995, 5 (04) :926-945

[8]

DENIS L, 1998, FORMES DIRICHLET ESP

[9]

FOLLMER H, 1993, ANN I H POINCARE-PR, V29, P569

[10]

Grorud A., 1998, INT J THEORETICAL AP, V01, P331, DOI [DOI 10.1142/S0219024998000199, 10.1142/S0219024998000199]

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