dual representation – Optimization Online

An Analytical Study of Norms and Banach Spaces Induced by the Entropic Value-at-Risk

Published: 2017/03/26, Updated: 2017/07/28

Finance and Economics, Robust Optimization, Stochastic Programming ^p$ spaces, coherent risk measures, donsker--varadhan variational formula, dual representation, kullback-leibler divergence, kusuoka representation, large deviations, moment and cumulant generating functions, orlicz and luxemburg norms, orlicz hearts and spaces, relative entropy

This paper addresses the Entropic Value-at-Risk (EVaR), a recently introduced coherent risk measure. It is demonstrated that the norms induced by EVaR induce the same Banach spaces, irrespective of the confidence level. Three spaces, called the primal, dual, and bidual entropic spaces, corresponding with EVaR are fully studied. It is shown that these spaces equipped … Read more

A Quantitative Comparison of Risk Measures

Published: 2015/09/14

Alois Pichler

Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming dual representation, risk measures

The choice of a risk measure reflects a subjective preference of the decision maker in many managerial, or real world economic problem formulations. To evaluate the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We … Read more