Details
| Original language | English |
|---|---|
| Pages (from-to) | 1505-1521 |
| Number of pages | 17 |
| Journal | Operations research |
| Volume | 58 |
| Issue number | 5 |
| Publication status | Published - Sept 2010 |
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, Exponential twisting, Importance sampling, Portfolio credit risk management, Shortfall risk, Stochastic approximation, Stochastic root finding
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Decision Sciences(all)
- Management Science and Operations Research
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In: Operations research, Vol. 58, No. 5, 09.2010, p. 1505-1521.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stochastic root finding and efficient estimation of convex risk measures
AU - Dunkel, Jörn
AU - Weber, Stefan
PY - 2010/9
Y1 - 2010/9
N2 - 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.
AB - 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.
KW - Convex risk measures
KW - Exponential twisting
KW - Importance sampling
KW - Portfolio credit risk management
KW - Shortfall risk
KW - Stochastic approximation
KW - Stochastic root finding
UR - http://www.scopus.com/inward/record.url?scp=77958459441&partnerID=8YFLogxK
U2 - 10.1287/opre.1090.0784
DO - 10.1287/opre.1090.0784
M3 - Article
AN - SCOPUS:77958459441
VL - 58
SP - 1505
EP - 1521
JO - Operations research
JF - Operations research
SN - 0030-364X
IS - 5
ER -