Optimal Unbiased Estimation for Expected Cumulative Cost
13 Pages Posted: 30 Apr 2018
Date Written: April 11, 2018
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
Suggested Citation: Suggested Citation