Backward stochastic differential equations with jumps and related nonlinear expectations (Q855683)

Consider real-valued backward stochastic differential equations with jumps together with their applications to nonlinear expectations, where the underlying filtration is generated by a Brownian motion and a Poisson random measure. The author studies comparison theorems and monotonicity of solutions of those equations. Additivity, inverse theorems, martingale-properties, and decomposition theorems are investigated among further properties of its solutions. The notions of \(f\)-expectations and nonlinear expectations are introduced. This paper can be understood in conjunction with the work of \textit{E. Pardoux} and \textit{S. G. Peng} [Syst. Control Lett. 14 , No. 1, 55--61 (1990; Zbl 0692.93064)].