On the importance function in splitting simulation

Thesplitting methodis a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is theImportance Function(IF). This function governs the placement of the thresholds or surfaces at which the paths are split We derive a characterisation of the optimal IF and show that for multi‐dimensional models the “natural” choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.