In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion (RGBSDE for short). The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a...

In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion (RGBSDE for short). The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a...

In this paper we extend the notion of “filtration-consistent nonlinear expectation” (or “F-consistent nonlinear expectation”) to the case when it is allowed to be dominated by a g-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental...

In this paper we study dynamic pricing mechanism of contingent claims. A typical model of such pricing mechanism is the so-called g-expectation $E^g_{s,t}[X]$ defined by the solution of the backward stochastic differential equation with generator g and with the contingent claim X as terminal...