We present a novel $Q$-learning algorithm to solve distributionally robust Markov decision problems, where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball around a (possibly estimated) reference measure.
In this paper, we extend the Wiener-Ito chaos decomposition to the class of diffusion processes, whose drift and diffusion coefficient are of linear growth.
We develop a new model for binary spatial random field reconstruction of a physical phenomenon which is partially observed via inhomogeneous time-series data.
We show how inter-asset dependence information derived from observed market prices of liquidly traded options can lead to improved model-free price bounds for multi-asset derivatives.
We present an approach, based on deep neural networks, that allows identifying robust statistical arbitrage strategies in financial markets.
We consider non-convex stochastic optimization problems where the objective functions have super-linearly growing and discontinuous stochastic gradients.
We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the determination of optimal hedging strategies attaining these bounds.
its marginals was recently established in Backhoff-Veraguas and Pammer  and Wiesel .
Probability Optimization and Control Mathematical Finance
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.
In this article we introduce and study a deep learning based approximation algorithm for solutions of stochastic partial differential equations (SPDEs).
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis.
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices.
Optimization and Control Probability Computational Finance Mathematical Finance Pricing of Securities
Hence we outperform the single-feature setting in Fischer & Krauss (2018) and Krauss et al. (2017) consisting only of the daily returns with respect to the closing prices, having corresponding daily returns of 0. 41% and of 0. 39% with respect to LSTM and random forests, respectively.
Ranked #1 on Stock Market Prediction on S&P 500
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning.
no code implementations • 17 Jan 2019 • Dominik Alfke, Weston Baines, Jan Blechschmidt, Mauricio J. del Razo Sarmina, Amnon Drory, Dennis Elbrächter, Nando Farchmin, Matteo Gambara, Silke Glas, Philipp Grohs, Peter Hinz, Danijel Kivaranovic, Christian Kümmerle, Gitta Kutyniok, Sebastian Lunz, Jan Macdonald, Ryan Malthaner, Gregory Naisat, Ariel Neufeld, Philipp Christian Petersen, Rafael Reisenhofer, Jun-Da Sheng, Laura Thesing, Philipp Trunschke, Johannes von Lindheim, David Weber, Melanie Weber
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results.
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications.
Numerical Analysis Probability