In this paper, we study the backward stochastic differential equations driven by a G-Brownian motion (Bt)t≥0 in the following form: Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt), where K is a decreasing G-martingale. Under Lipschitz conditions of f and g in Y and Z,...

A terminal perturbation method is introduced to study the backward approach to continuous time mean-variance portfolio selection with bankruptcy prohibition in a complete market model. Using Ekeland's variational principle, we obtain a necessary condition, i.e. the stochastic maximum principle,...

This paper investigates the relationships between coherent (convex) risk measures and Choquet expectations under the g-expectations framework. We deduce that convex risk measures can be dominated by Choquet expectations if, and only if they are coherent risk measures.

This paper proposes some new classes of risk measures, which are not only comonotonic subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order. We give their representations in terms of Choquet integrals w.r.t. distorted probabilities, and show that if the...

In this article, we consider the properties of hitting times for G-martingales and the stopped processes. We prove that the stopped processes for G-martingales are still G-martingales and that the hitting times for a class of G-martingales including one-dimensional G-Brownian motion are...