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Hinds, Piers D. (2025) Topics in stochastic numerics with applications in finance and optimization. PhD thesis, University of Nottingham.

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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:	Thesis (University of Nottingham only) (PhD)
Supervisors:	Tretyakov, Michael V. Bharath, Karthik
Keywords:	Stochastic differential equations, Monte Carlo, option pricing, variance reduction, jump-diffusions, reflected mean-field diffusion, interacting particle system, constrained optimization, consensus-based optimization, propagation of chaos
Subjects:	Q Science > QA Mathematics
Faculties/Schools:	UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID:	82821
Depositing User:	Hinds, Piers
Date Deposited:	12 Dec 2025 04:40
Last Modified:	12 Dec 2025 04:40
URI:	https://eprints.nottingham.ac.uk/id/eprint/82821

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