Abstract:  The generation of synthetic scenarios that mimic key characteristics of observed data has gained considerable attention as an important ingredient for risk estimation and the evaluation of trading strategies, among many other applications. In this talk, we will propose methods for both of these tasks. In the first part, based on joint work with Sam Cohen and Sheng Wang, we present a nonparametric model for the European options book based on neural SDEs, which respects underlying no-arbitrage constraints and is practically implementable. We study the inference problem where a model is learnt from discrete time series data of stock and option prices, and demonstrate its competitive performance for estimating risk measures. In the second part, based on joint work with Michael Giegrich and Roel Oomen, we propose a novel k-nearest neighbour resampling procedure for estimating the performance of a policy for a generic stochastic control problem from historical data containing realised episodes of a decision process generated under a different policy. We provide statistical consistency results under weak conditions in environments with continuous state-action spaces and system-inherent stochasticity affected by chosen actions. Numerical experiments exhibit a behaviour similar to Monte Carlo methods and demonstrate the effectiveness of the algorithm compared to existing baselines for trade execution in limit order books.

Bio: Christoph Reisinger is Professor of Applied Mathematics at the University of Oxford’s Mathematical Institute, where he currently serves as Director of Graduate Studies. His research interests include mathematical and computational finance, and, more broadly, stochastic modelling, computational mathematics, and the mathematical foundations of machine learning. He publishes regularly in journals such as the SIAM Journals on Control and Optimization and Financial Mathematics, Annals of Applied Probability, and Annals of Operations Research. He is Editor-in-Chief of The Journal of Computational Finance, recently served on the Senior Program Committee of the 4th ACM International Conference on AI in Finance (ICAIF23) and is on the Scientific Committees of the 5th International Conference on Computational Finance (ICCF24) and 12th World Congress of the Bachelier Finance Society.

Meeting Recording: https://ucsb.zoom.us/rec/share/33FPCoF8myBLlBUh2PfA1aBkofM3DDcaiGukZlSm87pKlYp2RzNiBvQcbXvZeEwf.dsuwCbyJ1g-BWwtC

Access Passcode: @&j6!pC9