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math.OC2026
Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach
Sebastian Kassing, Thomas Kruse
Stochastic gradient descent (SGD) has been studied extensively over the past decades due to its simplicity and broad applicability in machine learning. In this work, we analyze the…
math.OC2026
Time discretization of BSDEs with singular terminal condition using asymptotic expansion
Thomas Kruse, Julia Ackermann, Alexandre Popier
We consider a class of backward stochastic differential equations (BSDEs) with singular terminal condition and develop a numerical scheme to approximate their solution. To this end…
math.OC2026
Matrix Riccati BSDEs with singular terminal condition and stochastic LQ control with linear terminal constraint
Julia Ackermann, Thomas Kruse, Petr Petrov +1
We analyze a class of multidimensional linear-quadratic stochastic control problems with random coefficients, motivated by multi-asset optimal trade execution. The problems feature…