  We consider the problem where a modeller conducts sensitivity analysis of a
model consisting of random input factors, a corresponding random output of
interest, and a baseline probability measure. The modeller seeks to understand
how the model (the distribution of the input factors as well as the output)
changes under a stress on the output's distribution. Specifically, for a stress
on the output random variable, we derive the unique stressed distribution of
the output that is closest in the Wasserstein distance to the baseline output's
distribution and satisfies the stress. We further derive the stressed model,
including the stressed distribution of the inputs, which can be calculated in a
numerically efficient way from a set of baseline Monte Carlo samples and which
is implemented in the R package SWIM on CRAN.
  The proposed reverse sensitivity analysis framework is model-free and allows
for stresses on the output such as (a) the mean and variance, (b) any
distortion risk measure including the Value-at-Risk and Expected-Shortfall, and
(c) expected utility type constraints, thus making the reverse sensitivity
analysis framework suitable for risk models.
