A note on the doubly reflected backward stochastic differential equations driven by a Lévy process

2010 ◽  
Vol 80 (7-8) ◽  
pp. 690-696
Author(s):  
Xiliang Fan ◽  
Yong Ren ◽  
Dongjin Zhu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process

scholarly journals REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS

2009 ◽  
Vol 50 (4) ◽  
pp. 486-500 ◽  
Author(s):  
YONG REN ◽  
XILIANG FAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process ◽  
Penalization Method ◽  
Lower Semi ◽  
Uniqueness Of The Solution ◽  
Teugels Martingales ◽  
Continuous Convex Function

AbstractIn this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.

Reflected generalized BSDEs with discontinuous barriers driven by a Lévy process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed El Otmani
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process ◽  
Uniqueness Of The Solution ◽  
Teugels Martingales

Abstract This article deals with the reflected and doubly reflected generalized backward stochastic differential equations when the noise is given by Brownian motion and Teugels martingales associated with an independent pure jump Lévy process. We prove the existence and the uniqueness of the solution for these equations with monotone generators and right continuous left limited obstacles.

Some Properties of BSDEs Driven by a Simple Lévy Process with Continuous Coeffcient

2011 ◽  
Vol 50-51 ◽  
pp. 288-292
Author(s):  
Shi Qiu Zheng ◽  
Dian Chuan Jin ◽  
Shuai Zhang ◽  
Yan Mei Yang ◽  
Jin Peng Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Lévy Process ◽  
Linear Growth ◽  
Backward Stochastic Differential Equations ◽  
Levy Process

In this paper, we mainly study the properties of solutions of backward stochastic differential equations (BSDEs) driven by a simple Lévy process, whose coefficient coeffcient is continuous with linear growth. A comparison theorem for solutions of the equations are obtained, we also show the equation has either one or uncountably many solutions.

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