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  1. ; ; (, SIAM Journal on Financial Mathematics)
    Soner, Mete (Ed.)
    We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sub-linear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problem. Keywords. Deep neural networks, forward-backward systems of stochastic differential equations, optimal switching, Monte Carlo algorithm, optimal investment in power generation, planning problems 
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  2. ; (, SIAM Journal on Financial Mathematics)
    Soner, Mete (Ed.)
    For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Bj ̈ork and Murgoci (Finance Stoch, 2014) is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium policy exists if the objective is inf-compact in every time step. We provide a sufficient condition for the inf-compactness and thus existence, with costs that are lower semicontinuous (l.s.c.) and bounded from below and transition kernels that are continuous in controls under given states. The control spaces need not to be compact 
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