Aggregation-robustness and model uncertainty of regulatory risk measures

Finance and Stochastics - Tập 19 Số 4 - Trang 763-790 - 2015
Paul Embrechts1, Bin Wang2, Ruodu Wang3
1Department of Mathematics, RiskLab and SFI, ETH Zurich, Zurich, Switzerland
2Department of Mathematics, Beijing Technology and Business University, Beijing, China
3Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aas, K., Puccetti, G.: Bounds for total economic capital: the DNB case study. Extremes 17(4), 693–715 (2014)

Acerbi, C.: Spectral measures of risk: a coherent representation of subjective risk aversion. J. Bank. Finance 26, 1505–1518 (2002)

Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)

BCBS: Consultative Document May 2012. Fundamental review of the trading book. Basel Committee on Banking Supervision. Bank for International Settlements, Basel (2012). Available online http://www.bis.org/publ/bcbs219.htm

BCBS: Consultative Document October 2013. Fundamental review of the trading book: a revised market risk framework. Basel Committee on Banking Supervision. Bank for International Settlements, Basel (2013). Available online http://www.bis.org/publ/bcbs265.htm

Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)

Bernard, C., Jiang, X., Wang, R.: Risk aggregation with dependence uncertainty. Insur. Math. Econ. 54, 93–108 (2014)

Cambou, M., Filipović, D.: Model uncertainty and scenario aggregation. Math. Finance (2015, to appear). doi: 10.1111/mafi.12097

Cheung, K.C., Lo, A.: General lower bounds on convex functionals of aggregate sums. Insur. Math. Econ. 53, 884–896 (2013)

Cont, R., Deguest, R., Scandolo, G.: Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance 10, 593–606 (2010)

Daníelsson, J., Jorgensen, B.N., Mandira, S., Samorodnitsky, G., de Vries, C.G.: Subadditivity re-examined: the case for Value-at-Risk. Discussion paper, 549. Financial Markets Group, London School of Economics and Political Science. Available online http://eprints.lse.ac.uk/24668

EIOPA: Equivalence assessment of the Swiss supervisory system in relation to articles 172, 227 and 260 of the Solvency II Directive, EIOPA-BoS-11-028 (2011). Available online https://eiopa.europa.eu/Pages/SearchResults.aspx?k=filename:EIOPA-BoS-11-028-Swiss-Equivalence-advice.pdf

Embrechts, P., Puccetti, G.: Bounds for functions of dependent risks. Finance Stoch. 10, 341–352 (2006)

Embrechts, P., Puccetti, G., Rüschendorf, L.: Model uncertainty and VaR aggregation. J. Bank. Finance 37, 2750–2764 (2013)

Embrechts, P., Puccetti, G., Rüschendorf, L., Wang, R., Beleraj, A.: An academic response to Basel 3.5. Risks 2, 25–48 (2014)

Emmer, S., Kratz, M., Tasche, D.: What is the best risk measure in practice? A comparison of standard measures. Preprint, ESSEC Business School (2014). Available online http://ssrn.com/abstract=2370378

Föllmer, H., Schied, A.: Stochastic Finance: An Introduction in Discrete Time, 3rd edn. de Gruyter, Berlin (2011)

Gneiting, T.: Making and evaluating point forecasts. J. Am. Stat. Assoc. 106, 746–762 (2011)

Hampel, F.: A general qualitative definition of robustness. Ann. Math. Stat. 42, 1887–1896 (1971)

Hansen, L.P., Sargent, T.J.: Robustness. Princeton University Press, Princeton (2007)

Huber, P.J., Ronchetti, E.M.: Robust Statistics, 2nd edn. Wiley Series in Probability and Statistics. Wiley, New York (2009)

Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk, 3rd edn. McGraw-Hill, New York (2006)

Kou, S., Peng, X.: On the measurement of economic tail risk. Preprint (2014). Available online arXiv:1401.4787

Krätschmer, V., Schied, A., Zähle, H.: Qualitative and infinitesimal robustness of tail-dependent statistical functionals. J. Multivar. Anal. 103, 35–47 (2012)

Krätschmer, V., Schied, A., Zähle, H.: Comparative and quantitative robustness for law-invariant risk measures. Finance Stoch. 18, 271–295 (2014)

Kusuoka, S.: On law invariant coherent risk measures. Adv. Math. Econ. 3, 83–95 (2001)

Makarov, G.D.: Estimates for the distribution function of the sum of two random variables with given marginal distributions. Theory Probab. Appl. 26, 803–806 (1981)

Nelsen, R.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)

Puccetti, G.: Sharp bounds on the expected shortfall for a sum of dependent random variables. Stat. Probab. Lett. 83, 1227–1232 (2013)

Puccetti, G., Rüschendorf, L.: Sharp bounds for sums of dependent risks. J. Appl. Probab. 50, 42–53 (2013)

Puccetti, G., Rüschendorf, L.: Asymptotic equivalence of conservative value-at-risk- and expected shortfall-based capital charges. J. Risk 16(3), 1–19 (2014)

Puccetti, G., Wang, B., Wang, R.: Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates. Insur. Math. Econ. 53, 821–828 (2013)

Rüschendorf, L.: Random variables with maximum sums. Adv. Appl. Probab. 14, 623–632 (1982)

Sandström, A.: Handbook of Solvency for Actuaries and Risk Managers: Theory and Practice. Taylor & Francis, Florida (2010)

SCOR: From Principle-Based Risk Management to Solvency Requirements, 2nd edn. SCOR, Zurich (2008). SCOR Switzerland AG. Available online http://www.scor.com/images/stories/pdf/scorpapers/sstbook_second_edition_final.pdf

van der Vaart, A.W.: Asymptotic Statistics. Cambridge University Press, Cambridge (1998)

Wang, B., Wang, R.: The complete mixability and convex minimization problems for monotone marginal distributions. J. Multivar. Anal. 102, 1344–1360 (2011)

Wang, B., Wang, R.: Extreme negative dependence and risk aggregation. J. Multivar. Anal. 136, 12–25 (2015).

Wang, R.: Asymptotic bounds for the distribution of the sum of dependent random variables. J. Appl. Probab. 51, 780–798 (2014)

Wang, R., Peng, L., Yang, J.: Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities. Finance Stoch. 17, 395–417 (2013)

Wang, S.S., Young, V.R., Panjer, H.H.: Axiomatic characterization of insurance prices. Insur. Math. Econ. 21, 173–183 (1997)