An adaptive multilevel stochastic approximation scheme for Value-at-Risk computation achieves complexity O(ε^{-2} |ln ε|^{5/2}) by selecting inner samples adaptively at each level.
Weak error for nested multilevel Monte Carlo
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A multilevel stochastic approximation scheme achieves near-optimal complexity of order epsilon^{-2-delta} for VaR and epsilon^{-2}|ln epsilon|^2 for ES in nested risk estimation.
Establishes central limit theorems for the renormalized estimation errors of nested and multilevel stochastic approximation algorithms for VaR and ES, including averaged versions, with numerical illustration.
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Adaptive Multilevel Stochastic Approximation of the Value-at-Risk
An adaptive multilevel stochastic approximation scheme for Value-at-Risk computation achieves complexity O(ε^{-2} |ln ε|^{5/2}) by selecting inner samples adaptively at each level.
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Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall
Establishes central limit theorems for the renormalized estimation errors of nested and multilevel stochastic approximation algorithms for VaR and ES, including averaged versions, with numerical illustration.