Simulation input modeling: a kernel approach to estimating the density of a conditional expectation
Proceedings of the 35th conference on Winter simulation: driving innovation
Response surface methodology for simulating hedging and trading strategies
Proceedings of the 40th Conference on Winter Simulation
Nested Simulation in Portfolio Risk Measurement
Management Science
Sampling distribution of the variance
Winter Simulation Conference
Efficient Risk Estimation via Nested Sequential Simulation
Management Science
Input uncertainty in outout analysis
Proceedings of the Winter Simulation Conference
A quick assessment of input uncertainty
Proceedings of the Winter Simulation Conference
Stochastic kriging with biased sample estimates
ACM Transactions on Modeling and Computer Simulation (TOMACS)
| Hi-index | 0.00 |
In a two-level nested simulation, an outer level of simulation samples scenarios, while the inner level uses simulation to estimate a conditional expectation given the scenario. Applications include financial risk management, assessing the effects of simulation input uncertainty, and computing the expected value of gathering more information in decision theory. We show that an ANOVA-like estimator of the variance of the conditional expectation is unbiased under mild conditions, and we discuss the optimal number of inner-level samples to minimize this estimator's variance given a fixed computational budget. We show that as the computational budget increases, the optimal number of inner-level samples remains bounded. This finding contrasts with previous work on two-level simulation problems in which the inner-and outer-level sample sizes must both grow without bound for the estimation error to approach zero. The finding implies that the variance of a conditional expectation can be estimated to arbitrarily high precision by a simulation experiment with a fixed inner-level computational effort per scenario, which we call a one-and-a-half-level simulation. Because the optimal number of inner-level samples is often quite small, a one-and-a-half-level simulation can avoid the heavy computational burden typically associated with two-level simulation.