Sensitivity analysis via simulation in the presence of discontinuities

In this paper we address the problem of estimating the mean derivative when the entity containing the parameter has jumps. The methods considered are finite differences, infinitesimal perturbation analysis and the likelihood ratio score function. We calculate the difference between the differentiated mean and the mean derivative. In case of finite differences, we compute the stepsize in the simulation that asymptotically minimizes the mean square error. We also show that the two latter methods, infinitesimal perturbation analysis and likelihood ratio score function, are mathematically equivalent.