  We aim to analyze the behaviour of a finite-time stochastic system, whose
model is not available, in the context of more rare and harmful outcomes.
Standard estimators are not effective in making predictions about such outcomes
due to their rarity. Instead, we use Extreme Value Theory (EVT), the theory of
the long-term behaviour of normalized maxima of random variables. We quantify
risk using the upper-semideviation $\rho(Y) = E(\max\{Y - \mu,0\})$ of an
integrable random variable $Y$ with mean $\mu = E(Y)$. $\rho(Y)$ is the
risk-aware part of the common mean-upper-semideviation functional $\mu +
\lambda \rho(Y)$ with $\lambda \in [0,1]$. To assess more rare and harmful
outcomes, we propose an EVT-based estimator for $\rho(Y)$ in a given fraction
of the worst cases. We show that our estimator enjoys a closed-form
representation in terms of the popular conditional value-at-risk functional. In
experiments, we illustrate the extrapolation power of our estimator using a
small number of i.i.d. samples ($<$50). Our approach is useful for estimating
the risk of finite-time systems when models are inaccessible and data
collection is expensive. The numerical complexity does not grow with the size
of the state space.
