All Outputs (3)

Neural variance reduction for stochastic differential equations (2023)
Journal Article

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

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

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.