law invariance – Optimization Online

Distributionally Robust Stochastic Programming

Published: 2015/12/09, Updated: 2017/06/11

Robust Optimization, Stochastic Programming $\psihBcdivergence, chance constraints, coherent risk measures, law invariance, sample average approximation, wasserstein distance

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 consists of measures in some sense close to the reference measure. We discuss law invariance of the associated worst case functional and consider two basic constructions of such … Read more

On Kusuoka representation of law invariant risk measures

Published: 2011/09/15, Updated: 2012/05/14

Alexander Shapiro

Finance and Economics, Stochastic Programming average value at risk, coherent risk measures, comonotonic risk measures, fenchel-moreau theorem, law invariance

In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the Average Value-at-Risk measures. We show that such integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, … Read more