Stochastic Root Finding and Efficient Estimation of Convex Risk Measures

Jörn Dunkel () and Stefan Weber ()
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Jörn Dunkel: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
Stefan Weber: Institut für Mathematische Stochastik, Insurance and Financial Mathematics, Gottfried Wilhelm Leibniz Universität Hannover, 30167 Hannover, Germany

Operations Research, 2010, vol. 58, issue 5, 1505-1521

Abstract: 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.

Keywords: convex risk measures; shortfall risk; stochastic approximation; stochastic root finding; importance sampling; exponential twisting; portfolio credit risk management (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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