Asymptotics for operational risk quantified with a spectral risk measure

2012 ◽  
Vol 7 (3) ◽  
pp. 91-116 ◽  
Author(s):  
Bin Tong ◽  
Chongfeng Wu
Keyword(s):  
Risk Measure ◽  
Operational Risk ◽  
Spectral Risk Measure

Asymptotics for Operational Risk Quantified with Expected Shortfall

2009 ◽  
Vol 39 (2) ◽  
pp. 735-752 ◽  
Author(s):  
Francesca Biagini ◽  
Sascha Ulmer
Keyword(s):  
Confidence Level ◽  
Risk Measure ◽  
Operational Risk ◽  
Expected Shortfall ◽  
Dependence Structure ◽  
Practical Relevance ◽  
Convex Risk Measure ◽  
Multivariate Case ◽  
Univariate Case ◽  
Levy Copula

AbstractIn this paper we estimate operational risk by using the convex risk measure Expected Shortfall (ES) and provide an approximation as the confidence level converges to 100% in the univariate case. Then we extend this approach to the multivariate case, where we represent the dependence structure by using a Lévy copula as in Böcker and Klüppelberg (2006) and Böcker and Klüppelberg, C. (2008). We compare our results to the ones obtained in Böcker and Klüppelberg (2006) and (2008) for Operational VaR and discuss their practical relevance.

Fuzzy Risk Measure for Operational Risk

2018 ◽  
Vol 28 (1) ◽  
pp. 1-17
Author(s):  
Assem Tharwat ◽  
Ramadan ZeinEldin ◽  
Hamiden Khalifa ◽  
Ahmed Saleim
Keyword(s):  
Risk Measure ◽  
Operational Risk

Spectral risk measure minimization in hazardous materials transportation

2019 ◽  
Vol 51 (6) ◽  
pp. 638-652 ◽  
Author(s):  
Liu Su ◽  
Longsheng Sun ◽  
Mark Karwan ◽  
Changhyun Kwon
Keyword(s):  
Risk Measure ◽  
Hazardous Materials ◽  
Hazardous Materials Transportation ◽  
Spectral Risk Measure

scholarly journals Optimization Problem of Insurance Investment Based on Spectral Risk Measure and RAROC Criterion

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xia Zhao ◽  
Hongyan Ji ◽  
Yu Shi
Keyword(s):  
Risk Aversion ◽  
Optimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Attitude ◽  
Investment Strategy ◽  
Marginal Effect ◽  
Investment Ratio ◽  
Spectral Risk Measure ◽  
The Impact

This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment. Spectral risk measure could describe the degree of risk aversion, so the underlying strategy might take the investor's risk attitude into account. We establish an optimization model aiming at maximizing risk-adjusted return of capital (RAROC) involved with spectral risk measure. The theoretical result is derived and empirical study is displayed under different risk measures and different confidence levels comparatively. The result shows that risk attitude has a significant impact on investment strategy. With the increase of risk aversion factor, the investment ratio of risk asset correspondingly reduces. When the aversive level increases to a certain extent, the impact on investment strategies disappears because of the marginal effect of risk aversion. In the case of VaR and CVaR without regard for risk aversion, the investment ratio of risk asset is increasing significantly.

scholarly journals Spectral risk measure of holding stocks in the long run

2020 ◽  
Vol 295 (1) ◽  
pp. 75-89
Author(s):  
Zsolt Bihary ◽  
Péter Csóka ◽  
Dávid Zoltán Szabó
Keyword(s):  
Stock Price ◽  
Risk Measures ◽  
Risk Measure ◽  
Stable Process ◽  
Important Special Case ◽  
Finite Moment ◽  
Holding Period ◽  
Long Run ◽  
Spectral Risk Measures ◽  
Spectral Risk Measure

AbstractWe investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary exponential Lévy processes. We also prove the same behavior for all spectral risk measures (including the important special case of Expected Shortfall) when the stock price grows realistically fast and when it follows a geometric Brownian motion or a finite moment log stable process. This result would suggest that holding stocks for long periods has a vanishing downside risk. However, using realistic models, we find numerically that spectral risk initially increases for a significant amount of time and reaches zero level only after several decades. Therefore, we conclude that holding stocks has spectral risk for all practically relevant periods.

scholarly journals Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 50 ◽  
Author(s):  
Francesca Greselin ◽  
Fabio Piacenza ◽  
Ričardas Zitikis
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Sampling Error ◽  
Risk Measure ◽  
Simulated Data ◽  
Operational Risk ◽  
Computational Effort ◽  
Risk Measurement ◽  
Sampling Errors ◽  
Eu Regulation

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.

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