Zhipeng Huang , Balint Negyesi , Cornelis W. Oosterlee
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引用次数: 0
Abstract
It is well-known that decision-making problems from stochastic control can be formulated by means of a forward–backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. (2022) proposed an efficient deep learning algorithm based on the stochastic maximum principle (SMP). In this paper, we provide a convergence result for this deep SMP-BSDE algorithm and compare its performance with other existing methods. In particular, by adopting a strategy as in Han and Long (2020), we derive a-posteriori estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. We present numerical examples for high-dimensional stochastic control problems, both in the cases of drift- and diffusion control, which showcase superior performance compared to existing algorithms.
众所周知,随机控制的决策问题可以通过前向-后向随机微分方程(FBSDE)来表述。最近,Ji 等人(2022 年)提出了一种基于随机最大原则(SMP)的高效深度学习算法。在本文中,我们提供了这种深度 SMP-BSDE 算法的收敛结果,并将其性能与其他现有方法进行了比较。特别是,通过采用 Han 和 Long (2020) 的策略,我们得出了后验估计值,并证明总近似误差可由损失函数值和离散化误差限定。我们给出了高维随机控制问题的数值示例,包括漂移控制和扩散控制两种情况,与现有算法相比,这些示例展示了优越的性能。
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
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