We theoretically compare variances between the Infinitesimal Perturbation Analysis (IPA) estimator and the Likelihood Ratio (LR) estimator to Monte Carlo gradient for stochastic systems. The conditions proposed in [Cui et al., 2020] when the IPA estimator has a smaller variance can yield sharper...

The model-free e-backtesting method was recently introduced by Wang et al. (2022) to monitor the performance of risk measure forecasts. In order to provide more practical illustration and insights, this paper demonstrates detailed simulation and data analysis results on backtesting the...