# Reflected solutions of Anticipated Backward Doubly SDEs driven by Teugels Martingales

## TL;DR

This paper investigates reflected solutions and existence results for anticipated backward doubly stochastic differential equations driven by Teugels martingales, with coefficients depending on current and future solution values.

## Contribution

It introduces new existence results for anticipated BDSDEs driven by Teugels martingales with coefficients depending on future and present solutions.

## Key findings

- Established existence of solutions for anticipated BDSDEs
- Analyzed reflected solutions under Lipschitz conditions
- Extended theory to equations driven by Teugels martingales

## Abstract

We deal with reflected solutions of anticipated backward doubly stochastic differential equations (RABDSDEs) driven by Teugels martingales associated with L\'evy process under a Lipschitz generator where the coefficients of these BDSDEs depend on the future and present value of the solution $\left( Y,Z\right) $. Also we study the existence of a solution for anticipated BDSDEs.