zbMATH — the first resource for mathematics

Robustness and sensitivity analysis of risk measurement procedures. (English) Zbl 1192.91191
Summary: Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a “risk measure” that summarizes the risk of the portfolio. We define the notion of “risk measurement procedure”, which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical value-at-risk. We also propose alternative risk measurement procedures that possess the robustness property.

91G70 Statistical methods; risk measures
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI
[1] DOI: 10.1016/S0378-4266(02)00281-9
[2] DOI: 10.1080/14697680701461590 · Zbl 1190.91071
[3] DOI: 10.1111/1467-9965.00068 · Zbl 0980.91042
[4] Costa V, Asterisque pp 43– (1977)
[5] DOI: 10.1016/j.jempfin.2006.09.004
[6] DOI: 10.1007/s11408-006-0002-x
[7] Deniau C, Asterisque pp 43– (1977)
[8] DOI: 10.1111/j.1539-6975.2008.00264.x
[9] DOI: 10.1007/s007800200072 · Zbl 1041.91039
[10] DOI: 10.1515/9783110212075
[11] DOI: 10.1016/S0378-4266(02)00270-4
[12] DOI: 10.1016/S0927-5398(00)00011-6
[13] Gourieroux C, Working Paper (2006)
[14] Hampel F, Robust Statistics: The Approach Based on Influence Functions (1986)
[15] Heyde, C, Kou, S and Peng, X. 2007. ”What is a good risk measure: bridging the gaps between data, coherent risk measures, and insurance risk measures”. Columbia University. Preprint
[16] DOI: 10.1002/0471725250 · Zbl 0536.62025
[17] DOI: 10.1016/j.jbankfin.2006.11.014
[18] Kusuoka S, Adv. Math. Econ. 3 pp 83– (2001)
[19] DOI: 10.1016/S0378-4266(02)00271-6
[20] Tasche D, Statistical Data Analysis Based on the L1-Norm and Related Methods pp 109– (2002)
[21] DOI: 10.1214/aop/1176994626 · Zbl 0448.60025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.