Inference under threshold uncertainty

Develop the conditional Wasserstein generative adversarial network methodology to incorporate uncertainty in the Pareto severity threshold by assigning the threshold a prior distribution.

Background

The severity model assumes a fixed threshold x_min and uses the Pareto shape parameter as the latent parameter of interest. Under this specification, the log-excesses above the threshold yield a one-dimensional sufficient statistic for posterior inference.

The paper does not address uncertainty about the threshold itself. The authors explicitly propose assigning the threshold a prior, which would enlarge the inferential parameter space and require the amortized posterior approximation to account for the jointly uncertain threshold and Pareto shape parameter.