优化中的风险四方:附有近期成果和扩展的概览

The Risk Quadrangle in Optimization: An Overview with Recent Results and Extensions

This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four stochastics-oriented functionals -- risk, deviation, regret, and error, along with an associated statistic, and articulates their revealing and in some ways surprising interrelationships and dualizations. Additions to the RQ framework that have come to light since 2013 are re