Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Acceleration of stochastic approximation by averaging
SIAM Journal on Control and Optimization
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Computational Optimization and Applications
Fast simulation for multifactor portfolio credit risk in the t-copula model
WSC '05 Proceedings of the 37th conference on Winter simulation
Efficient Monte Carlo methods for convex risk measures in portfolio credit risk models
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Robust Stochastic Approximation Approach to Stochastic Programming
SIAM Journal on Optimization
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Reliable risk measurement is a key problem for financial institutions and regulatory authorities. The current industry standard Value-at-Risk has several deficiencies. Improved risk measures have been suggested and analyzed in the recent literature, but their computational implementation has largely been neglected so far. We propose and investigate stochastic approximation algorithms for the convex risk measure Utility-Based Shortfall Risk. Our approach combines stochastic root-finding schemes with importance sampling. We prove that the resulting Shortfall Risk estimators are consistent and asymptotically normal, and provide formulas for confidence intervals. The performance of the proposed algorithms is tested numerically. We finally apply our techniques to the Normal Copula Model, which is also known as the industry model CreditMetrics. This provides guidance for future implementations in practice.