This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …

When estimating the risk of a P&L from historical data or Monte Carlo simulation, the
robustness of the estimate is important. We argue here that Hampel's classical notion of …

We address the statistical estimation of composite functionals which may be nonlinear in the
probability measure. Our study is motivated by the need to estimate coherent measures of …

The performance of ML models degrades when the training population is different from that
seen under operation. Towards assessing distributional robustness, we study the worst-case …

We provide a variety of results for quasiconvex, law-invariant functionals defined on a
general Orlicz space, which extend well-known results from the setting of bounded random …

We consider bilevel linear problems, where the right-hand side of the lower level problems
is stochastic. The leader has to decide in a here-and-now fashion, while the follower has …

We consider a two-stage stochastic bilevel linear program where the leader contemplates
the follower's reaction at the second stage optimistically. In this setting, the leader's objective …

We introduce three new families of reward-risk ratios, study their properties and compare
them with existing examples. All ratios in the three families are monotonic and …

When estimating the risk of a financial position with empirical data or Monte Carlo
simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at …

We apply a suitable modification of the functional delta method to statistical functionals that
arise from law-invariant coherent risk measures. To this end we establish differentiability of …