Quantile of a Mixture with Application to Model Risk Assessment

• Autorzy: Carole Bernard , Steven Vanduffel
• Języki publikacji: EN

Abstrakty

EN

We provide an explicit expression for the quantile of a mixture of two random variables. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial dependence information is available. This paper complements the work of [4].

Słowa kluczowe

EN

Model Risk; Rearrangement Algorithm; Mixture

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings
• 60E05: Distributions: general theory

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-06-16

zaakceptowano

2015-10-14

online

2015-10-27

Twórcy

autor

Carole Bernard

• Department of Accounting, Law and Finance at the Grenoble Ecole de Management

autor

Steven Vanduffel

• Department of Economics and Political Sciences at Vrije Universiteit Brussel
  (VUB)

Bibliografia

• [1] Acerbi, C., and D. Tasche (2002). On the coherence of expected shortfall. J. Banking Financ. 26(7), 1487–1503.
• [2] Bernard, C., L. Rüschendorf, and S. Vanduffel (2015). VaR bounds with a variance constraint. Forthcoming in J. Risk Insurance.
• [3] Bernard, C., L. Rüschendorf, S. Vanduffel, and J. Yao (2015). How Robust is the Value-at-Risk of Credit Risk Portfolios? Forthcoming in Eur. J. Financ.
• [4] Bernard, C., and S. Vanduffel (2015). A new approach to assessing model risk in high dimensions, J. Banking Financ. 58, 166–178.
• [5] Castellacci, G. (2012). A formula for the quantiles of mixtures of distributions with disjoint supports. Available at http:// ssrn.com/abstract=2055022.
• [6] Embrechts, P., G. Puccetti, and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Banking Financ. 37(8), 2750–2764. [WoS]
• [7] Föllmer, H., and A. Schied (2011): Stochastic Finance: an Introduction in Discrete Time. Walter de Gruyter, Berlin.
• [8] Gaffke, N., and L. Rüschendorf (1981). On a class of extremal problems in statistics. Optimization 12(1), 123–135.
• [9] Kotz, S., and S. Nadarajah (2004). Multivariate t-distributions and their Applications. Cambridge University Press.
• [10] Landsman, Z. M., and E. A. Valdez (2003). Tail conditional expectations for elliptical distributions. North Amer. Actuar. J. 7(4), 55–71.
• [11] McNeil, A. J., R. Frey, and P. Embrechts (2005): Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press.
• [12] Puccetti, G., and L. Rüschendorf (2013). Sharp bounds for sums of dependent risks. J. Appl. Probab. 50(1), 42–53. [Crossref][WoS]
• [13] Puccetti, G., B. Wang, and R. Wang (2012). Advances in complete mixability. J. Appl. Probab. 49(2), 430–440. [Crossref]
• [14] Puccetti, G., B. Wang, and R. Wang (2013). Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates. Insurance Math. Econom. 53(3), 821–828.
• [15] Wang, B., and R. Wang (2011). The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102(10), 1344–1360. [WoS]

Identyfikatory

DOI

10.1515/demo-2015-0012