Revista de Matemática Aplicada e Computacional

Adaptive Multilevel Splitting Method for Rare Event Estimation

Abstract

Josephine Frankfort*

Rare event estimation is crucial in many fields, such as finance, engineering, and environmental science. These events, although infrequent, can have significant consequences, making their accurate prediction and understanding vital. Traditional methods often fall short due to the immense computational power required or lack of accuracy. The Adaptive Multilevel Splitting (AMS) method offers a robust alternative, providing a practical approach to estimating the probability of rare events in complex systems. The core of the AMS method is its splitting mechanism, where simulations that reach a certain intermediate threshold are duplicated. This process enhances the sampling of rare events, increasing the likelihood of observing them without requiring an excessive number of initial simulations. Define the rare event of interest and the corresponding threshold. Initialize a large number of independent simulations. Run the simulations until they reach the predefined threshold or fail. The successful paths are then analyzed to determine the next threshold. Simulations that reach the threshold are split, creating multiple copies that are slightly perturbed. This step increases the sample size for subsequent levels.