Quantile of a Mixture with Application to Model Risk Assessment

Carole Bernard; Steven Vanduffel

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 172-181, electronic only
  • ISSN: 2300-2298

Abstract

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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].

How to cite

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Carole Bernard, and Steven Vanduffel. "Quantile of a Mixture with Application to Model Risk Assessment." Dependence Modeling 3.1 (2015): 172-181, electronic only. <http://eudml.org/doc/275983>.

@article{CaroleBernard2015,
abstract = {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].},
author = {Carole Bernard, Steven Vanduffel},
journal = {Dependence Modeling},
keywords = {Model Risk; Rearrangement Algorithm; Mixture; model risk; rearrangement algorithm; mixture},
language = {eng},
number = {1},
pages = {172-181, electronic only},
title = {Quantile of a Mixture with Application to Model Risk Assessment},
url = {http://eudml.org/doc/275983},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Carole Bernard
AU - Steven Vanduffel
TI - Quantile of a Mixture with Application to Model Risk Assessment
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 172
EP - 181, electronic only
AB - 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].
LA - eng
KW - Model Risk; Rearrangement Algorithm; Mixture; model risk; rearrangement algorithm; mixture
UR - http://eudml.org/doc/275983
ER -

References

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  1. [1] Acerbi, C., and D. Tasche (2002). On the coherence of expected shortfall. J. Banking Financ. 26(7), 1487–1503. 
  2. [2] Bernard, C., L. Rüschendorf, and S. Vanduffel (2015). VaR bounds with a variance constraint. Forthcoming in J. Risk Insurance. 
  3. [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. [4] Bernard, C., and S. Vanduffel (2015). A new approach to assessing model risk in high dimensions, J. Banking Financ. 58, 166–178. 
  5. [5] Castellacci, G. (2012). A formula for the quantiles of mixtures of distributions with disjoint supports. Available at http:// ssrn.com/abstract=2055022. 
  6. [6] Embrechts, P., G. Puccetti, and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Banking Financ. 37(8), 2750–2764. [WoS] 
  7. [7] Föllmer, H., and A. Schied (2011): Stochastic Finance: an Introduction in Discrete Time. Walter de Gruyter, Berlin. Zbl1126.91028
  8. [8] Gaffke, N., and L. Rüschendorf (1981). On a class of extremal problems in statistics. Optimization 12(1), 123–135. Zbl0467.60004
  9. [9] Kotz, S., and S. Nadarajah (2004). Multivariate t-distributions and their Applications. Cambridge University Press. Zbl1100.62059
  10. [10] Landsman, Z. M., and E. A. Valdez (2003). Tail conditional expectations for elliptical distributions. North Amer. Actuar. J. 7(4), 55–71. Zbl1084.62512
  11. [11] McNeil, A. J., R. Frey, and P. Embrechts (2005): Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. Zbl1089.91037
  12. [12] Puccetti, G., and L. Rüschendorf (2013). Sharp bounds for sums of dependent risks. J. Appl. Probab. 50(1), 42–53. [Crossref][WoS] Zbl1282.60017
  13. [13] Puccetti, G., B. Wang, and R. Wang (2012). Advances in complete mixability. J. Appl. Probab. 49(2), 430–440. [Crossref] Zbl1245.60020
  14. [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. Zbl1290.62019
  15. [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] Zbl1229.60019

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