In this talk, we consider the signature-to-path reconstruction problem from the control theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $L^2$-norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $\Gamma$-converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.
Marco Rauscher started his undergraduate studies in October 2015 and obtained his bachelor’s degree from TUM in 2018. Afterwards he began his master’s program in the field of mathematics with a strong focus on “finance” and “machine learning”. During his master’s program Marco spent one semester abroad at the University of Lund in Sweden. Moreover, he gathered practical experience as an intern at the Bayerische Landesbank. For his master’s thesis on machine learning in the field of VIX related products he participated in the iCAIR research project and collaborated with the University of Toronto. Since he has finished his master’s degree, he is a PhD candidate at the Technical University of Munich with Prof. Horvath as his mentor.
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