Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator

@article{Zhang2022BackwardSD,
  title={Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator},
  author={Peiguo Zhang and A. I. N. Ibrahim and Nur Anisah Mohamed},
  journal={Axioms},
  year={2022},
  volume={11},
  pages={536}
}
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the solution are established using Yosida approximations. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite… 

References

SHOWING 1-10 OF 27 REFERENCES

Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality

We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes,

Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality

We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes,

L p solutions of Backward Stochastic Dierential Equations

In this paper we are interested in solving backward stochastic dierential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of

BSDEs driven by infinite dimensional martingales and their applications to stochastic optimal control

Abstract In this paper we consider a backward stochastic differential equation driven by an infinite dimensional martingale. Our aim is to derive the existence and uniqueness of the solution to such

Numerical schemes for multivalued backward stochastic differential systems

AbstractWe define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for

BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets

We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the

Multi‐valued backward stochastic differential equations driven by G‐Brownian motion and its applications

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G‐Brownian motion with subdifferential operator by means of the

$L^{p}$ - Variational Solution of Backward Stochastic Differential Equation driven by subdifferential operators on a deterministic interval time

−dYt + ∂yΨ(t, Yt) dQt ∋ H (t, Yt, Zt) dQt − ZtdBt, t ∈ [0, T ] , YT = η, where Q is a progresivelly measurable increasing continuous stochastic process and ∂yΨ is the subdifferential of the convex

Anticipated Generalized Backward Doubly Stochastic Differential Equations

In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two