Higher order elicitability and Osband's principle Page 1 The Annals of Statistics 2016, Vol. 44,
No. 4, 1680–1707 DOI: 10.1214/16-AOS1439 © Institute of Mathematical Statistics, 2016 …

This is a substantial revision of the previous edition with added new material. The
presentation of Chapter 6 is updated. In particular the Interchangeability Principle for risk …

The topic of this book is multistage stochastic optimization. Multistage reflects the fact that an
optimal decision is an entire strategy or policy, which is executed during subsequent instants …

The risk of a financial position is usually summarized by a risk measure. As this risk measure
has to be estimated from historical data, it is important to be able to verify and compare …

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually
superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues …

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 …

Mean field game theory is devoted to the analysis of differential games with a (very) larger
number of “small” players. By “small” player, we mean a player who has very little influence …

The quantification of downside risk in terms of capital requirements is a key issue for both
regulators and the financial industry. This review presents the axiomatic approach, which is …

In this paper we study distributionally robust stochastic programming in a setting where there
is a specified reference probability measure and the uncertainty set of probability measures …

This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing.
The book is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced …