Dynamic stochastic optimisation generally suffers from the curse of dimensionality as state spaces grow exponentially in dimension and in the number of periods. Particle methods for filtering and smoothing, however, maintain a fixed number of states in each period and can converge to a posterior distribution using Markov Chain Monte Carlo methods. This talk will discuss how this approach can be applied in the context of dynamic stochastic optimisation and conditions for convergence to an optimal solution.
John R. Birge studies mathematical modelling of systems under uncertainty, especially for maximising operational and financial goals using the methodologies of stochastic programming and large-scale optimisation. He was first drawn to this area by a need to use mathematics in a useful and practical way. This research has been supported by the National Science Foundation, the Ford Motor Company, General Motors Corporation, the National Institute of Justice, the Office of Naval Research, the Electric Power Research Institute, and Volkswagen of America. He has published widely and is the recipient of the Best Paper Award from the Japan Society for Industrial and Applied Mathematics, the Institute for Operations Research and the Management Sciences Fellows Award, the Institute of Industrial Engineers Medallion Award and was elected to the National Academy of Engineering. A former dean of the Robert R. McCormick School of Engineering and Applied Sciences at Northwestern University, he has worked as a consultant for a variety of firms including the University of Michigan Hospitals, Deutsche Bank, Allstate Insurance Company, and Morgan Stanley, and he uses cases from these experiences in his teaching. Birge earned a bachelor’s degree in mathematics from Princeton University in 1977 and a master’s degree and a PhD in operations research from Stanford University in 1979 and 1980, respectively. He joined the Chicago Booth faculty in 2004. He is a member of the Institute for Operations Research and the Management Sciences, the Mathematical Programming Society, the Mathematical Association of America, and Sigma Xi. He also speaks French, Russian, German, and English.
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