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ABOUT REGULARISATION OF THE WEIGHTED AVERAGE MONTE CARLO METHOD

Galimnurov Artur Albertovich  (Postgraduate Ufa University of Science and Technology )

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.
 

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Citation link:
Galimnurov A. A. ABOUT REGULARISATION OF THE WEIGHTED AVERAGE MONTE CARLO METHOD // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2025. -№05/2. -С. 43-46 DOI 10.37882/2223-2966.2025.05-2.06
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