Coherent Approaches to Risk in Optimization Under Uncertainty

By Terry Rockafellar. 2007

305 citations recorded by the source corpus.

Decisions often need to be made before all the facts are in. A facility must be built to withstand storms, floods, or earthquakes of magnitudes that can only be guessed from historical records. A portfolio must be purchased in the face of only statistical knowledge, at best, about how markets will perform. In optimization, this implies that constraints may need to be envisioned in terms of safety margins instead of exact requirements. But what does that really mean in model formulation? What guidelines make sense, and what are the consequences for optimization structure and computation? The idea of a coherent measure of risk in terms of surrogates for potential loss, which has been developed in recent years for applications in financial engineering, holds promise for a far wider range of applications in which the traditional approaches to uncertainty have been subject to criticism. The general ideas and main facts are presented here with the goal of facilitating their transfer to practical work in those areas.

Subfields: Finance, Management Science and Operations Research, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/b42006f002d324c9f137b38a058e20250448f5d1

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Citations in the corpus

Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization (2008, methodology): “Deviation Measures In this section, we refer to Rockafellar [17] and Rockafellar et al.”
Distributionally Robust Optimization: A Review (2019, background): “For detailed discussions of the duality theory in infinite-dimensional convex problems, we refer to Rockafellar [257], and we refer to Isii [162] and Shapiro [284] for duality theory in conic linear programs.”
Risk-sensitive Inverse Reinforcement Learning via Coherent Risk Models (2017, background): “These metrics were introduced in the operations research literature and have played an influential role within the modern theory of risk in finance [40, 4, 3, 39].”
Modeling and solving a large-scale generation expansion planning problem under uncertainty (2011, methodology): “This metric is known as Conditional Value-at-Risk, or CVaR [51,54].”
Incorporating risk measures in closed-loop supply chain network design (2014, background): “These approaches are completely developed and discussed in Rockafellar, Uryasev, and Zabarankin (2006) and Rockafellar (2007).”
Fairness risk measures (2019, background): “Per Rockafellar [2007, Equation 5.8], as α → 1, (21) becomes min i.e., we seek all subgroup risks to be small, per the maximin principle [Rawls, 1971].”
Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives (2016, background): “There are many risk measures that are widely used in practice, such as the variance of the loss distribution, shortfall probability, downside risk, and value-at-risk (VaR) (Rockafellar, 2007).”
An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011, methodology): “Dentcheva and Ruszczyński (2006) transform (23) into a set of linear constraints by introducing new variables to represent positive parts.”