Mind the jumps: well-posedness of semi-martingale 2BSDEs

Abstract

We develop a well-posedness theory for second-order backward stochastic differential equations (2BSDEs) with jumps. This work covers two complementary notions of solution: an extrinsic and an intrinsic one. We also discuss the obstruction to aggregating jump integrands. The chosen framework allows for controlled diffusions with jumps, pure-jump processes, and discrete-time processes in a unified setting.

arXiv comment51 pages. This manuscript is Part II of a two-part work; Part I is arXiv:2609.25126