Simulating Discounted Costs

We numerically estimate, via simulation, the expected infinite-horizon discounted cost d of running a stochastic system. A naive strategy estimates a finite-horizon approximation to d. We propose alternatives. All are ranked with respect to asymptotic variance as a function of computer-time budget and discount rate, when semi-Markov and/or regenerative structure or neither is assumed. In this setting, the naive truncation estimator loses; it may triumph, however, when the computer-time budget is modest, the discount rate is large, and the process simulated is not regenerative or has long cycle lengths.