The concepts of risk aversion, chance-constrained optimization, and robust optimization
have developed significantly over the last decade. The statistical learning community has …

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 …

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry
and regulatory standard for the calculation of risk capital in banking and insurance. This …

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-
Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes …

In mean-risk portfolio optimization, it is typically assumed that the assets follow a known
distribution P 0, which is estimated from observed data. Aiming at an investment strategy …

This paper proposes general methods for the problem of multiple testing of a single
hypothesis, with a standard goal of combining a number of-values without making any …

Research related to aggregation, robustness and model uncertainty of regulatory risk
measures, for instance, value-at-risk (VaR) and expected shortfall (ES), is of fundamental …

In quantitative risk management, it is important and challenging to find sharp bounds for the
distribution of the sum of dependent risks with given marginal distributions, but an …

Risk aggregation with dependence uncertainty refers to the sum of individual risks with
known marginal distributions and unspecified dependence structure. We introduce the …

The probabilistic characterization of the relationship between two or more random variables
calls for a notion of dependence. Dependence modeling leads to mathematical and …