Before revision:  As their multivariate density is generally not available for more than three locations, the likelihood ratio method cannot be used to estimate the derivatives of the risk measures with respect to the model parameters . Thus, we focus on a pathwise method, the infinitesimal perturbation analysis (IPA). We provide a convenient and tractable sufficient condition for performing IPA , which is intricate to obtain because of the very structure of max-stable fields involving pointwise maxima over an infinite number of random functions.
After revision:  As their multivariate density is generally not available for more than three locations, the likelihood ratio method cannot be used to estimate the derivatives of the risk measures with respect to the parameters for each simulated value. We propose convenient and tractable sufficient condition for performing IPA , which is intricate to obtain because of the very structure of max-stable fields involving pointwise maxima over an infinite number of random functions.