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 "martingale condition" instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization.The solution of this equation consists of a triplet of processes (Y, Z, K). The existence and uniqueness of the solution are proved in [10]. In [11] the comparison theorem, Feymann-Kac formula and some related topics associated with this kind of G-BSDEs were established.In this paper, we study the case where the solution of a G-BSDE is required to stay above a given stochastic process, called the lower obstacle. An increasing process should be added in this equation to push the solution upwards, so that it may remain above the obstacle. According to the classical case studied by [5], we may expect that the solution of reflected G-BSDE is a quadrupleThe shortcoming is that the solution of the above problem is not unique. Thus, to get the uniqueness of the reflected G-BSDE, we should reformulate this problem as the following. A triplet of processes (Y, Z, A) is called a solution of reflected G-BSDE if the following properties hold:is a non-increasing G-martingale. Here, we denote by S α G (0, T ) the collection of process (Y, Z, A) such that Y ∈ S α G (0, T ), Z ∈ H α G (0, T ), A is a continuous nondecreasing process with A 0 = 0 and A ∈ S α G (0, T ). Note that we use a "martingale condition" (c) instead of the Skorohod condition. Under some appropriate assumptions, we can prove that the solution of the above reflected G-BSDE is unique. In proving the existence of this problem, we should use the approximation method via penalization. This is a constructive method in the sense that the solution of the reflected G-BSDE is proved to be the limit of a sequence of penalized G-BSDEs. Different from the classical case, the dominated convergence theorem does not hold under G-framework. Besides, any bounded sequence in M p G (0, T ) is no longer weakly compact. The main difficulty in carrying out this construction is to prove the convergence property in some appropriate sense. It is worth pointing out that the main idea is to apply the uniformly continuous property of the elements in S p G (0, T ). Actually, the above equations hold P -a.s. for every probability measure P belongs to a nondominated class of mutually singular measures. Therefore, the G-expectation theory shares many similarities with second order BSDEs (2BSDEs for short) developed by Cheridito, Soner, Touzi and Victoir [1]. Matoussi, Possamai and Zhou [21] showed the existence and uniqueness of second order reflected BSDE whose solution is (Y, Z, K P ) P ∈P κ H satisfyingwith Y t ≥ S t , K P t − k P t = ess inf P P ′ ∈PH (t+,P ) E P ′ t [K P T − k P T ], P -a.s., 0 ≤ t ≤ T, ∀P ∈ P κ H ,
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