Restricted risk measures and robust optimization

Restricted risk measures and robust optimization

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 cl...

Robust Discrete Optimization and Downside Risk Measures

We propose methods for robust discrete optimization in which the objective function has cost components that are subject to independent and bounded perturbations. Motivated by risk management practice, we approximate the problem of optimization of VaR, a widely used downside risk measure by introducing four approximating models that origininate in robust optimization. We show that all four mode...

Risk measures and robust optimization problems

These lecture notes give a survey on recent developments in the theory of risk measures. The first part outlines the general representation theory of risk measures in a static one-period setting. In particular, it provides structure theorems for law-invariant risk measures. Examples include Value at Risk, Average Value at Risk, distortion risk measures, and risk measures arising from robust pre...

Restricted Coherent Risk Measures and Actuarial Solvency

Ambiguous Risk Measures and Optimal Robust Portfolios

This paper deals with a problem of guaranteed (robust) financial decision-making under model uncertainty. An efficient method is proposed for determining optimal robust portfolios of risky financial instruments in the presence of ambiguity (uncertainty) on the probabilistic model of the returns. Specifically, it is assumed that a nominal discrete return distribution is given, while the true dis...