A Pooled Quantile Estimator for Parallel Simulations

Quantile is an important risk measure quantifying the stochastic system random behaviors. This paper studies a pooled quantile estimator, which is the sample quantile of detailed simulation outputs after directly pooling independent sample paths together. We derive the asymptotic representation of the pooled quantile estimator and further prove its normality. By comparing with the classical quantile estimator used in stochastic simulation, both theoretical and empirical studies demonstrate the advantages of the proposal under the context of parallel simulation.