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- handle: 10670/1.ah8mcj
- hal: hal-03352812
- ARXIV: 2007.14659
- doi: 10.1214/21-EJP648
- WOS: 000669504900004
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info:eu-repo/semantics/altIdentifier/arxiv/2007.14659
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1214/21-EJP648
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Mots-clés
Stochastic approximation Quantile and superquantile Conditional value-at-risk Limit theoremsSujets proches
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Bernard Bercu et al., « Stochastic approximation algorithms for superquantiles estimation », HAL-SHS : économie et finance, ID : 10.1214/21-EJP648
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Résumé
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 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.