Title: Neural Markov Controlled SDE: Stochastic Optimization for Continuous-Time Data. Abstract: We propose a novel probabilistic framework for modeling stochastic dynamics with the rigorous use of stochastic optimal control theory. The proposed model called the neural Markov controlled stochastic differential equation (CSDE) overcomes the fundamental and structural limitations of conventional dynamical models by introducing the following two components: (1) Markov dynamic programming to efficiently train the proposed CSDE and (2) multi-conditional forward-backward losses to provide rich information for accurate inference and to assure theoretical optimality. We demonstrate that our dynamical model efficiently generates a complex time series in the data space without extra networks while showing comparable performance against existing model-based methods on several datasets.