ABOUT REGULARISATION OF THE WEIGHTED AVERAGE MONTE CARLO METHOD

Galimnurov Artur Albertovich

Within the framework of this paper, we propose a formulation of a regularised variant (RWMLMC) of the weighted multilevel Monte Carlo (WMLMC) method, introducing a penalty term to control the magnitude of the level-dependent weights and stabilise the contribution of the variance between levels. While classical WMLMC can lead to unstable or highly variable weights when inter-level correlations are weak, RWMLMC introduces a tunable regularisation parameter λ that provides robustness and improved generalisation in the presence of noise or unbalanced simulations. We empirically analyse the performance of the proposed method, showing that RWMLMC achieves a better trade-off between cost and variance and improves performance in realistic multilevel sampling regimes.

Keywords:Monte Carlo methods, financial modelling, regularization.