Abstract: In the first part of the talk, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilises a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.

In the second part of the talk, we propose an extension of the Deep BSDE solver by E, Han and Jentzen (2017) to the case of FBSDEs with jumps. As in the aforementioned solver, starting from a discretized version of the BSDE and parametrizing the (high dimensional) control processes by means of a family of ANNs, the BSDE is viewed as model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity, introducing in the latest case, an approximation with finitely many jumps of the forward process.

This talk is based on joint works with A. Picarelli and C. Reisinger (first part) A. Picarelli and M. Patacca (second part)

Bio: Alessandro Gnoatto is an associate professor of Financial Mathematics at the University of Verona. His research interests include multiple curve interest rate and cross currency models, counterparty credit risk and funding, computational finance, machine learning methods for PDEs, and affine processes.

Before joining the University of Verona, he held positions as counterparty credit risk front office quant at BayernLB, postdoc in the Workgourp Financial Mathematics at the LMU Munich and risk management analyst at Prometeia SpA.

He holds a PhD in Computational Mathematics from the University of Padova and an MSc in Quantitative Finance from ETH/University of Zurich.

Meeting Recording: https://ucsb.zoom.us/rec/share/MraEcy1gP1-vu9774DuH0wpPQFzsmyhSFsjG3w7eL_gLXCEDda1oPyt_z2OEk1ds.RoSfH20HlHsQ8uDS

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