Tensor-Train Solvers for High-Dimensional PDEs and Multi-Asset Option Pricing

PhD defence by Lucas Silva Arenstein

Assessment Committee

Associate Professor Albert Werner, Mathematics, University of Copenhagen (Chairperson)
Research Scientist Edwin Miles Stoudenmire, Flatiron Institute, Center for Computational Quantum Physics
Research Director Xavier Waintal, University of Grenoble

Supervisors

Associate Professor Michael Kastoryano

Department

Department of Computer Science

Place

Building: Niels Bohr Institute, Room: Aud. D 02-0-Ca12, Blegdamsvej 17, 2100 Copenhagen

Email address to gain access to the thesis: lsa@di.ku.dk.
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Short description of the thesis

Many scientific and financial problems become difficult when the number of variables grows, because the calculations can require impractically large amounts of data and computation.
This thesis investigates tensor-train methods: mathematical tools that compress large numerical objects into smaller, reusable representations. It develops two complementary approaches for pricing financial options that depend on several assets. One approach numerically solves a high-dimensional differential equation and retains option values across a grid of asset prices; the other uses Fourier–cosine methods based on characteristic functions for a range of market models. The results show how a single high-dimensional computation can support later pricing and the calculation of risk sensitivities (Greeks), provided that the underlying problem has sufficient compressible structure.