Efficient Computation for Stratified Splitting

Many applications in the areas of finance, environments, service systems, and statistical learning require the computation for a general function of the expected performances associated with one or many random objects. When complicated stochastic systems are involved, such computation needs to be done by stochastic simulation and the computational cost can be expensive. We design simulation algorithms that exploit the common random structure shared by all random objects, referred to as stratified splitting. We discuss the optimal simulation budget allocation problem for the proposed algorithms. A brief numerical experiment is conducted to illustrate the performance of the proposed algorithm with various budget allocation rules.