Outputs (18)

Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing (2024)
Journal Article
Su, H., Tretyakov, M. V., & Newton, D. P. (2024). Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing. Management Science, https://doi.org/10.1287/mnsc.2022.01448

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equat... Read More about Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing.

Neural variance reduction for stochastic differential equations (2023)
Journal Article
Hinds, P., & Tretyakov, M. (2023). Neural variance reduction for stochastic differential equations. Journal of Computational Finance, 27(3), 1-41. https://doi.org/10.21314/JCF.2023.010

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately... Read More about Neural variance reduction for stochastic differential equations.

Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions (2023)
Journal Article
Leimkuhler, B., Sharma, A., & Tretyakov, M. V. (2023). Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions. Annals of Applied Probability, 33(3), 1904-1960. https://doi.org/10.1214/22-AAP1856

A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo techniq... Read More about Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions.

Consensus-based optimization via jump-diffusion stochastic differential equations (2023)
Journal Article
Kalise, D., Sharma, A., & Tretyakov, M. V. (2023). Consensus-based optimization via jump-diffusion stochastic differential equations. Mathematical Models and Methods in Applied Sciences, 33(02), 289-339. https://doi.org/10.1142/S0218202523500082

We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). We study well-posedness of the particle system as well as of its mean-field limit.... Read More about Consensus-based optimization via jump-diffusion stochastic differential equations.

Ensemble Kalman inversion for magnetic resonance elastography. (2022)
Journal Article
Iglesias, M., McGrath, D. M., Tretyakov, M. V., & Francis, S. T. (2022). Ensemble Kalman inversion for magnetic resonance elastography. Physics in Medicine and Biology, 67(23), Article 235003. https://doi.org/10.1088/1361-6560/ac9fa1

Magnetic Resonance Elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this pape... Read More about Ensemble Kalman inversion for magnetic resonance elastography..

Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light (2022)
Journal Article
Endruweit, A., Matveev, M., & Tretyakov, M. V. (2022). Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light. Polymer Composites, 43(11), 8308-8321. https://doi.org/10.1002/pc.27001

A vacuum infusion process was implemented to produce composite specimens from a random glass filament mat and an acrylic modified polyester resin curable upon irradiation with ultraviolet (UV) light. Through localized irradiation with UV light during... Read More about Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light.

Bayesian inversion algorithm for estimating local variations in permeability and porosity of reinforcements using experimental data (2021)
Journal Article
Matveev, M., Endruweit, A., Long, A., Iglesias, M., & Tretyakov, M. (2021). Bayesian inversion algorithm for estimating local variations in permeability and porosity of reinforcements using experimental data. Composites Part A: Applied Science and Manufacturing, 143, Article 106323. https://doi.org/10.1016/j.compositesa.2021.106323

Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation (2020)
Journal Article
Milstein, G. N., & Tretyakov, M. V. (2021). Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation. Numerical Mathematics, 14(1), 1-30. https://doi.org/10.4208/nmtma.OA-2020-0034

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals r... Read More about Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation.

Effect of random forcing on fluid lubricated bearing (2019)
Journal Article
Bailey, N., Hibberd, S., Tretyakov, M., & Power, H. (2019). Effect of random forcing on fluid lubricated bearing. IMA Journal of Applied Mathematics, 84(3), 632–649. https://doi.org/10.1093/imamat/hxz007

A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation... Read More about Effect of random forcing on fluid lubricated bearing.

Bayesian inversion in resin transfer molding (2018)
Journal Article
Iglesias, M., Park, M., & Tretyakov, M. (2018). Bayesian inversion in resin transfer molding. Inverse Problems, 34(10), Article 105002. https://doi.org/10.1088/1361-6420/aad1cc

We study a Bayesian inverse problem arising in the context of Resin Transfer Molding (RTM), which is a process commonly used for the manufacturing of fiber- reinforced composite materials. The forward model is described by a moving boundary problem i... Read More about Bayesian inversion in resin transfer molding.