Levy-type stochastic integrals with regularly varying tails

被引：5

作者：

Applebaum, D ^{[1
]}

机构：

[1] Univ Sheffield, Dept Probabil & Stat, Sheffield S3 7RH, S Yorkshire, England

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2005年 / 23卷 / 03期

关键词：

Levy measure; Levy-type stochastic integral; predictable mapping; regular variation; semimartingale;

D O I：

10.1081/SAP-200056692

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Levy-type stochastic integrals M = (M(t), t >= 0) are obtained by integrating suitable predictable mappings against Brownian motion B and an independent Poisson random measure N. We establish conditions under which teh right tails of M are of regular variation. In particular, we require that the intensity measure associated to N is the product of a regularly varying Levy measure with Lebesgue measure. Both univariate and multivariate versions of the problem are considered.

引用

页码：595 / 611

页数：17

共 21 条

[1] THE STABLE-LAW MODEL OF STOCK RETURNS [J].

AKGIRAY, V ;

BOOTH, GG .

JOURNAL OF BUSINESS & ECONOMIC STATISTICS, 1988, 6 (01) :51-57

[2]

Applebaum D., 2004, LEVY PROCESSES STOCH

[3] Regular variation of GARCH processes [J].

Basrak, B ;

Davis, RA ;

Mikosch, T .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 99 (01) :95-115

[4]

Bingham N. H., 1987, Regular Variation

[5] SUBEXPONENTIALITY AND INFINITE DIVISIBILITY [J].

EMBRECHTS, P ;

GOLDIE, CM ;

VERAVERBEKE, N .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1979, 49 (03) :335-347

[6] COMPARING THE TAIL OF AN INFINITELY DIVISIBLE DISTRIBUTION WITH INTEGRALS OF ITS LEVY MEASURE [J].

EMBRECHTS, P ;

GOLDIE, CM .

ANNALS OF PROBABILITY, 1981, 9 (03) :468-481

[7]

Embrechts P., 1980, J AUSTR MATH SOC A, V29, P243, DOI DOI 10.1017/S1446788700021224

[8]

Embrechts P., 1997, MODELLING EXTREMAL E, DOI 10.1007/978-3-642-33483-2

[9]

Feller W., 1971, An introduction to probability theory and its applications, VII

[10]

Ikeda N., 1989, STOCHASTIC DIFFERENT, DOI DOI 10.1002/BIMJ.4710320720

← 1 2 3 →