Optimal Unbiased Estimation for Expected Cumulative Cost

Abstract

We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. Numerical experiments substantiate the theoretical results.

Keywords: unbiased simulation, optimal control, cumulative cost, efficiency of estimator

JEL Classification: C61, C63