Topics in stochastic numerics with applications in finance and optimization
Publication Date
December 12, 2025
Creator
Abstract
This thesis is devoted to the study of two topics related to the application of numerical solution of stochastic differential equations (SDEs). First, we consider variance reduction for Lévy-driven SDEs. We develop optimality conditions for the variance reduction and propose a numerical algorithm for efficient variance reduction. The algorithm makes use of a neural network in order to approximate a control variate. Several numerical examples from option pricing are presented.
Second, we study reflected McKean-Vlasov SDEs in smooth bounded domains, for which we prove well-posedness and propagation of chaos. We also consider their application to constrained optimization problems via consensus-based optimization (CBO). We propose two CBO models, for which numerical approximation schemes correspond to constrained optimization algorithms. We test the performance of these algorithms on benchmark optimization problems as well as on an inverse problem.
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
82821
UoN Repository URI
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