Backward stochastic variational inequalities with locally bounded generators

TL;DR

This paper establishes existence and uniqueness results for backward stochastic variational inequalities with locally bounded generators, expanding the theoretical understanding of such stochastic systems.

Contribution

It introduces new conditions for existence and uniqueness of solutions when the generator function is only locally bounded.

Findings

Proves existence of solutions under local boundedness conditions.

Establishes uniqueness of solutions in the specified setting.

Provides a framework for analyzing backward stochastic variational inequalities with less restrictive assumptions.

Abstract

The paper deals with the existence and uniqueness of the solution of the backward stochastic variational inequality: \begin{equation} \left\{\begin{array} {l}-dY_{t}+\partial \varphi(Y_{t})dt \ni F(t,Y_{t},Z_{t})dt-Z_{t}dB_{t},\;0\leq t<T \\ Y_{T}=\eta, \end{array} \right.\end{equation} where $F$ satisfies a local boundedness condition.