Stochastic approximation algorithms for superquantiles estimation

This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile, also known as conditional value-at-risk, estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified version. Our main contribution establish almost sure convergence, quadratic strong law iterated logarithm our estimates via martingale approach. A joint normality provided. theoretical analysis illustrated by numerical experiments on real datasets.