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