A BSDE approach to the Skorokhod embedding problem for the Brownian motion with drift

被引：6

作者：

Ankirchner, Stefan ^{[1
]}

Heyne, Gregor ^{[1
]}

Imkeller, Peter ^{[1
]}

机构：

[1] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

来源：

STOCHASTICS AND DYNAMICS | 2008年 / 8卷 / 01期

关键词：

Skorokhod embedding; Brownian motion; diffusion; stopping time; control theory; BSDE; quadratic growth; Malliavin calculus;

D O I：

10.1142/S0219493708002160

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：

We solve Skorokhod's embedding problem for Brownian motion with linear drift (W-t + kappa t)(t >= 0) by means of techniques of stochastic control theory. The search for a stopping time T such that the law of W-T + kappa T coincides with a prescribed law mu possessing the first moment is based on solutions of backward stochastic differential equations of quadratic type. This new approach generalizes an approach by Bass [3] of the classical version of Skorokhod's embedding problem using martingale representation techniques.

引用

页码：35 / 46

页数：12

共 12 条

[1]

ANKIRCHNER S, MATH07053788V1

[2]

Azema J., 1979, LECT NOTES MATH, P90, DOI 10.1007/BFb0070852

[3]

BASS RF, 1983, SEM PROBAB STRASBOUR, V17, P221

[4]

BRIAND P, MATH0703423V1