MINIMAL SUPERSOLUTIONS OF CONVEX BSDES

被引：22

作者：

Drapeau, Samuel ^{[1
]}

Heyne, Gregor ^{[1
]}

Kupper, Michael ^{[1
]}

机构：

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

来源：

ANNALS OF PROBABILITY | 2013年 / 41卷 / 06期

关键词：

Supersolutions of backward stochastic differential equations; nonlinear expectations; supermartingales; STOCHASTIC DIFFERENTIAL-EQUATIONS; G-BROWNIAN MOTION; RISK MEASURES; CALCULUS; THEOREM;

D O I：

10.1214/13-AOP834

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 study the nonlinear operator of mapping the terminal value xi to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in y, convex in z, jointly lower semicontinuous and bounded below by an affine function of the control variable z. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.

引用

页码：3973 / 4001

页数：29

共 36 条

[1] Classical and varitional differetiability of BSDEs with quadratic growth [J].