Restricted risk measures and robust optimization

Abstract

In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of random parameters, we may consider some new variants of the uncertainty sets determined by the classical characterizations. We also show that in the finite probability case these variants are simple transformations of the classical sets. Finally we present results of computational experiments that suggest that the risk measures associated with these new uncertainty sets can help mitigate estimation errors of the Conditional Value-at-Risk.

Generalized Adaptive Partition-based Method for Two-Stage Stochastic Programs with Fixed Recourse

“…Case study: For the computational test, we solve the classic portfolio problem, where x represents the fraction of the portfolio assigned to each investment and the constraints of the first stage are x e = 1, x ≥ 0, ensuring to invest the whole budget in non-negative fractions. Additionally, we assume that returns r of each investment follow a multivariate normal distribution rξ N (µ, Σ) using historical data for stocks listed on the SP500, as in [30] and [9].…”