Abstract: A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several examples related to financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

Bio: Mete Soner is a Professor of Operations Research and Financial Engineering at Princeton University, also affiliated with the Bendheim Center of Finance and with the Program in Applied & Computation Mathematics.

Mete's research is on decisions under uncertainty and related problems in stochastic optimal control, Markov decision processes, nonlinear partial differential equations, probability theory, mathematical finance, and financial economics. He has co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, and authored or co-authored 100+ articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control, and mathematical finance.

Currently, he is Editor-in-Chief of SIAM Journal of Financial Mathematics (SIFIN), a Co-Editor of Mathematics and Financial Economics (MAFE), and an associate editor for Finance and Stochastics, Interfaces and Free Boundaries, Mathematics of Operations Research. During 2011-2016, he has been the Executive Secretary of the Bachelier Finance Society. In 2014, he received an Alexander von Humbolt Foundation Research Award. In 2015, he was elected as a SIAM Fellow.

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