<i>g</i>-Expectation for Conformable Backward Stochastic Differential Equations

Abstract

In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.

Keywords

• nonlinear expectation
• <i>g</i>-expectation
• Doob–Meyer decomposition theorem