Unbiased Monte Carlo computation of smooth functions of expectations via Taylor expansions

Many Monte Carlo computations involve computing quantities that can be expressed as g(EX), where g is nonlinear and smooth, and X is an easily simulatable random variable. The nonlinearity of g makes the conventional Monte Carlo estimator for such quantities biased. In this paper, we show how such quantities can be estimated without bias. However, our approach typically increases the variance. Thus, our approach is primarily of theoretical interest in the above setting. However, our method can also be applied to the computation of the inner expectation associated with Eg ((EX|Z)), and in this setting, the application of this method can have a significant positive effect on improving the rate of convergence relative to conventional “nested schemes” for carrying out such calculations.