Conditional value‐at‐risk beyond finance: a survey

A large number of problems involve making decisions in an uncertain environment and, hence, with unknown outcomes. Optimization models aimed at controlling the trade‐off between risk and return in finance have been widely studied since the seminal work by Markowitz in 1952. In financial applications, shortfall or quantile risk measures are receiving ever‐increasing attention. Conditional value‐at‐risk (CVaR) is arguably the most popular of such measures. In the last decades, optimization models aimed at controlling risk have been applied to several application domains different from financial optimization. This survey provides an overview of the main contributions where CVaR is incorporated into an optimization approach and applied to a context different from financial engineering. The literature is classified following an application‐oriented perspective. The applications cover classical areas studied in operational research—such as supply chain management, scheduling, and networks—and less classical areas such as energy and medicine. For each area, concise paper excerpts are provided that convey the main ideas of the problems studied, and analyze how the CVaR has been used to cope with different sources of uncertainty. Finally, some open research directions are outlined.