Abstract
We study the solution of one-dimensional generalized backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing, and bounded, we prove the existence of a solution.
Highlights
A linear version of backward stochastic differential equations (BSDEs) was first studied by Bismut [4] as the adjoint processes in the maximum principal of stochastic control
We study the solution of one-dimensional generalized backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion
Pardoux and Peng in [20] introduced the notion of nonlinear BSDE
Summary
A linear version of backward stochastic differential equations (BSDEs) was first studied by Bismut [4] as the adjoint processes in the maximum principal of stochastic control. BSDEs provide connection with mathematical finance [10], stochastic control [11], and stochastic game [9]. This class of BSDEs is a powerful tool to give probabilistic formulas for solution of partial differential equations (see [18, 19]). Consider the nonlinear BSDE: T. where ξ is an ᏲT -measurable random variable that will become certain only at the terminal time T, and f is a progressively measurable process. In [20], the authors showed that there exists a unique Ᏺt-adapted process (Y ,Z) solution of the BSDE (1.1), when the coefficient f is Lipschitz in y and z, ξ is square integrable.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Applied Mathematics and Stochastic Analysis
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
