Inverse Optimization of Convex Risk Functions

The theory of convex risk functions has now been well established as the basis for identifying families that should be used in risk-averse optimization problems. Despite its theoretical appeal, implementation a function remains difficult, because there is little guidance regarding how chosen so it also represents decision maker’s subjective preference. In this paper, we address issue through lens inverse optimization. Specifically, given solution data from some (forward) problem (i.e., minimization with known constraints), develop an framework generates renders solutions optimal forward problem. incorporates well-known properties functions—namely, monotonicity, convexity, translation invariance, and law invariance—as general information about candidate functions, feedback individuals—which include initial estimate pairwise comparisons among random losses—as more specific information. Our particularly novel unlike classical optimization, does not require making any parametric assumption nonparametric). We show resulting problems can reformulated programs are polynomially solvable if corresponding solvable. illustrate imputed portfolio selection demonstrate their practical value using real-life data. This paper was accepted by Yinyu Ye,