Star-Shaped Risk Measures

In this paper, monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties are studied. The measures in this class, which a…

Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Mea…

Inspired by the recent developments in risk sharing problems for the value at risk (VaR), the expected shortfall (ES), and the range value at risk (RVaR), we study the optimization of risk sharing …

Robustness in the Optimization of Risk Measures

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk-measurement-related optimization…

Distributional Transforms, Probabilty Distortions, and Their Applications

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimi…

A Theory for Measures of Tail Risk

The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehen…

An Axiomatic Foundation for the Expected Shortfall

Characterization, Robustness, and Aggregation of Signed Choquet Integrals