AIMS Lab Seminar - Anastasis Kratsios - Universal Regular Conditional Distributions for High-Dimensional Option Pricing and Constrained Learning
Title: Universal Regular Conditional Distributions for High-Dimensional Option Pricing and Constrained Learning
Abstract: Regular conditional distributions (RCDs) are of central importance to most areas of applied probability, ranging from mathematical finance to uncertainty quantification in machine learning. Nevertheless, there is currently no available universal class of deep neural models capable of approximating any RCD. We fill this theoretical gap by proposing a new geometric deep learning model with inputs in a Euclidean and outputs in the Wasserstein space over a Euclidean space. Our models can, with arbitrarily high probability, uniformly approximate the regular conditional distributions. Our results are all framed in the context of pricing high-dimensional portfolios of options in mathematical finance. Our results are then applied to derive the first solution to the problem of universal approximation under exact non-convex constraints. We then briefly discuss the general case of polish spaces.
Date/Time: Monday October 18 2021, 11:30am - 12:20pm
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Meeting ID: 925 7896 5537