Stochastic Root Finding and Efficient Estimation of Convex Risk Measures

• 成果类型: Article
• 署名作者: Dunkel, Joern; Weber, Stefan
• 署名单位: University of Oxford; Leibniz University Hannover
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1090.0784
• 发表日期: 2010
• 页码: 1505-1521
• 关键词: average approximation method

摘要

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.