  Consider a newsvendor problem with an unknown demand distribution. When
addressing the issue of distributional uncertainty, we distinguish ambiguity
under which the newsvendor does not differentiate demand distributions of
common distributional characteristics (e.g., mean and variance) and
misspecification under which such characteristics might be misspecified (due
to, e.g., estimation error and/or distribution shift). The newsvendor hedges
against ambiguity and misspecification by maximizing the worst-case expected
profit regularized by a distribution's distance to an ambiguity set of
distributions with some specified characteristics. Focusing on the popular
mean-variance ambiguity set and optimal-transport cost for the
misspecification, we show that the decision criterion of misspecification
aversion possesses insightful interpretations as distributional transforms and
convex risk measures. We derive the closed-form optimal order quantity that
generalizes the solution of the seminal Scarf model under only ambiguity
aversion. This highlights the impact of misspecification aversion: the optimal
order quantity under misspecification aversion can decrease as the price or
variance increases, reversing the monotonicity of that under only ambiguity
aversion. Hence, ambiguity and misspecification, as different layers of
distributional uncertainty, can result in distinct operational consequences. We
quantify the finite-sample performance guarantee, which consists of two parts:
the in-sample optimal value and the out-of-sample effect of misspecification
that can be decoupled into estimation error and distribution shift. This
theoretically justifies the necessity of incorporating misspecification
aversion in a non-stationary environment, which is also well demonstrated in
our experiments with real-world retailing data.
