Unifying constructions of martingales associated with processes increasing in the convex order, via Levy and Sato sheets

被引：6

作者：

Hirsch, Francis ^{[1
]}

Roynette, Bernard ^{[2
]}

Yor, Marc ^{[3
,4
]}

机构：

[1] Univ Evry Val Essonne, Lab Anal & Probabil, F-91025 Evry, France

[2] Univ Henri Poincare, Inst Math Elie Cartan, F-54506 Vandoaeuvre Les Nancy, France

[3] Univ Paris 6 & 7, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France

[4] Inst Univ France, Paris, France

来源：

EXPOSITIONES MATHEMATICAE | 2010年 / 28卷 / 04期

关键词：

BROWNIAN-MOTION; MARGINALS; SPACE;

D O I：

10.1016/j.exmath.2010.04.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present a unified framework for our previous constructions of martingales with the same one-dimensional marginals as particular cases of processes increasing in the convex order. This framework encompasses our former uses of Levy sheets, Sato sheets and self-decomposable laws. New examples of processes increasing in the convex order are also exhibited, but we do not know how to associate to them martingales with the same one-dimensional marginals. (C) 2010 published by Elsevier GmbH.

引用

页码：299 / 324

页数：26

共 20 条

[1]

[Anonymous], STOCHASTIC PROCESS A

[2] A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. [J].

Baker, D. ;

Yor, M. .

ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 :1532-1540

[3] Iterates of the infinitesimal generator and space-time harmonic polynomials of a Markov process [J].

Barrieu, P ;

Schoutens, W .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 186 (01) :300-323

[4] On the qualitative effect of volatility and duration on prices of Asian options [J].

Carr, Peter ;

Ewald, Christian-Oliver ;

Xiao, Yajun .

FINANCE RESEARCH LETTERS, 2008, 5 (03) :162-171

[5] THE SHARP MARKOV PROPERTY OF LEVY SHEETS [J].

DALANG, RC ;

WALSH, JB .

ANNALS OF PROBABILITY, 1992, 20 (02) :591-626

[6]

FUKUSHIMA M, 1984, J MATH SOC JPN, V36, P161, DOI 10.2969/jmsj/03610161

[7] Looking for martingales associated to a self-decomposable law [J].

Hirsch, F. ;

Yor, M. .

ELECTRONIC JOURNAL OF PROBABILITY, 2010, 15 :932-961

[8]

HIRSCH F, J MATH SOC IN PRESS

[9]

HIRSCH F, 2010, PERIOD MATH HUNG, V61, P203

[10] A construction of processes with one-dimensional martingale marginals, associated with a Levy process, via its Levy sheet [J].

Hirsch, Francis ;

Yor, Marc .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2009, 49 (04) :785-815

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