g-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.

Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator

“…As a result, BSDEs have developed rapidly, whether in their own development or in many other related fields such as financial mathematics, stochastic control, biology, the financial futures market, the theory of partial differential equations, and stochastic games. Reference can be made to Karoui et al [2], Hamadene and Lepeltial [3], Peng [4,5], Ren and Xia [6], and Luo et al [7], among others. Among the BSDEs, Pardoux and Rȃşcanu [8] considered BSDEs involving a subdifferential operator, which are also dubbed Backward Stochastic Variational Inequalities (BSVIs), and also utilized them with the Feymann-Kac formula to represent a solution of the multivalued parabolic partial differential equations (PDEs).…”