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In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum condition, we reformulate the original control problem as a new one. Three algorithms are proposed to solve the new control problem. Numerical results for different examples demonstrate the effectiveness of our proposed algorithms, especially in high dimensional cases. And an important application of this method is to calculate the sub-linear expectations, which correspond to a kind of fully nonlinear PDEs.
This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on Bellmans dynami
In this paper, the optimal control problem of neutral stochastic functional differential equation (NSFDE) is discussed. A class of so-called neutral backward stochastic functional equations of Volterra type (VNBSFEs) are introduced as the adjoint equ
In this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter into all the
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in
We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a risk functi