Kalman filters have found use in many applications across engineering, finance, economics, and a host of other fields. The linear Gaussian assumption required to make them work, however, is rather restrictive. Krishnan et.al. (2015) introduce a variation where the observed and latent states evolution are non-linear transformations using a deep neural net called Deep Kalman Filters (DKFs). Here, we develop a reinforcement learning architecture combining probabilistic inference for learning control with DKF to solve stochastic control problems in environments without assumptions on model dynamics. The method is data efficient, robust to noisy and incomplete data, and results in superior performance in comparison to a number of other state-of-the-art methods applied to an optimal execution problem.
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Sebastian Jaimungal is a Professor and the current Director of the professional Masters of Financial Insurance program in the Department of Statistical Sciences of University of Toronto, and he teaches in the Mathematical Finance Program, as well as the PhD and MSc programs in the Department of Statistical Sciences. He consults for major banks and hedge funds focusing on implementing advance derivative valuation engines and algorithmic trading strategies. He is also a Managing Editor of Quantitative Finance, an Associate Editor for the SIAM Journal on Financial Mathematics, the International Journal of Theoretical and Applied Finance, High Frequency, Journal of Risks and Argo. Jaimungal is the current Chair (former Vice Chair; former Program Director) for the SIAM activity group on Financial Engineering and Mathematics, and his research has been widely published in academic and practitioner journals. Moreover, he was a founding board member of the Commodities and Energy Markets Association and now serve on its advisory board. His recent interests include high-frequency and algorithmic trading, applied stochastic control, mean-field games, real options, and commodity models and derivative pricing.