Actuarial Science and Financial Mathematics seminar series
Stanislav Uryasev
Stony Brook University
Room: M3 3127
Risk Quadrangle and Applications in Statistics, Data Mining, and Portfolio Optimization
A quadrangle includes four functions quantifying uncertainty: Risk, Deviation, Regret, and Error. These functions are interconnected with one more function called Statistic. We consider several quadrangles: Expectile, Superquantile Norm, Symmetric Quantile Average, f-Divergence. The quadrangle framework results in many new analytical results. For instance, we show that Support Vector Regression is an asymptotically unbiased estimator of the average of two symmetric conditional quantiles and that Conditional Value-at-Risk, Expectile, and Omega portfolio optimization are equivalent.
The paper reviews recent results obtained with the Risk Quadrangle Framework.