Since the seminal work of Mann and Picard in 1994, the standard way to build high dynamic range (HDR) images from regular cameras has been to combine a reduced number of photographs captured with different exposure times. The algorithms proposed in the literature differ in the strategy used to combine these frames. Many experimental studies comparing their performances have been reported, showing in particular that a maximum likelihood estimation yields the best results in terms of mean squared error. However, no theoretical study aiming at establishing the performance limits of the HDR estimation problem has been conducted. Another common aspect of all HDR estimation approaches is that they discard saturated values. In this paper, we address these two issues. More precisely, we derive theoretical bounds for the HDR estimation problem, and we show that, even with a small number of photographs, the maximum likelihood estimator (MLE) performs extremely close to these bounds. As a second contribution, we propose a general strategy to integrate the information provided by saturated pixels in the estimation process, hence improving the estimation results. Finally, we analyze the sensitivity of the HDR estimation process to camera parameters, and we show that small errors in the camera calibration process may severely degrade the estimation results.