MMN-3766

A class of conformable backward stochastic differential equations with jumps

  • Mei Luo, Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P. R. China, meiluomath@163.com
  • JinRong Wang, Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P. R. China, jrwang@gzu.edu.cn
  • Donal O' Regan, National University of Ireland, Galway, Ireland, donal.oregan@nuigalway.ie

Abstract

In this paper, we study conformable backward stochastic differential equations driven by a Brownian motion and a compensated random measure. We derive the conformable It\^{o}'s formula with jumps and a priori estimates and we obtain the existence and uniqueness of solutions under some assumptions in the framework of the conformable derivative. In addition we get a predictable representation of the solution. Comparison theorems for the operator $g$ under different conditions are given. We also establish the inverse comparison theorem for the operator $g$ under a Lipschitz condition.


Vol. 23 (2022), No. 2, pp. 811-845
DOI: 10.18514/MMN.2022.3766


Download: MMN-3766