Existence, minimality and approximation of solutions to BSDEs with convex drivers

被引：9

作者：

Cheridito, Patrick ^{[1
]}

Stadje, Mitja ^{[2
,3
]}

机构：

[1] Princeton Univ, Princeton, NJ 08544 USA

[2] Tilburg Univ, NL-5000 LE Tilburg, Netherlands

[3] CentER, Tilburg, Netherlands

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 04期

基金：

美国国家科学基金会;

关键词：

Backward stochastic differential equations; Backward stochastic difference equations; Convex drivers; Discrete-time approximations; Supersolutions; QUADRATIC BSDES; GENERATORS; EQUATIONS;

D O I：

10.1016/j.spa.2011.12.008

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 existence of solutions to backward stochastic differential equations with drivers f(t, W, y, z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y, Z) with bounded Z if the terminal condition is Lipschitz in W and that it can be approximated by the solutions to properly discretized equations. If the terminal condition is bounded and uniformly continuous in W we show the existence of a minimal continuous supersolution by uniformly approximating the terminal condition with Lipschitz terminal conditions. Finally, we prove the existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions. (c) 2011 Elsevier B.V. All rights reserved.

引用

页码：1540 / 1565

页数：26

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