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In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the representation theorem of G-expectation and weak convergence to obtain the regularity of fully nonlinear PDE associated to G-BSDE. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under G-expectation. Under standard assumptions, we establish the comparison theorem for this kind of BSDE and give a novel and simple method to obtain the dynamic programming principle. Finally, we prove that the value function is the unique viscosity solution to a type of fully nonlinear HJB equation. [ABSTRACT FROM AUTHOR]

For backward stochastic differential equations (BSDEs), we construct a fully explicit multi-step time-discretization scheme and prove its stability and convergence rates. To approximate conditional expectations in our scheme, we design a new algorithm based on the multilevel Monte Carlo (MLMC) method. This estimator can achieve a prescribed error ϵ with a computational effort of order ϵ − 2. Numerical experiments are given to illustrate the theoretical results of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal wealth and portfolio is the solution of a forward-backward stochastic differential equation with constraints. [Copyright &y& Elsevier]