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Risk measurement in the presence of background risk

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  • Tsanakas, Andreas

Abstract

A distortion-type risk measure is constructed, which evaluates the risk of any uncertain position in the context of a portfolio that contains that position and a fixed background risk. The risk measure can also be used to assess the performance of individual risks within a portfolio, allowing for the portfolio's re-balancing, an area where standard capital allocation methods fail. It is shown that the properties of the risk measure depart from those of coherent distortion measures. In particular, it is shown that the presence of background risk makes risk measurement sensitive to the scale and aggregation of risk. The case of risks following elliptical distributions is examined in more detail and precise characterisations of the risk measure's aggregation properties are obtained.

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  • Tsanakas, Andreas, 2008. "Risk measurement in the presence of background risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 520-528, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:520-528
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    References listed on IDEAS

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    Cited by:

    1. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, vol. 1(1), pages 1-20, March.
    2. Shuo Gong & Yijun Hu & Linxiao Wei, 2022. "Distortion risk measures in random environments: construction and axiomatic characterization," Papers 2211.00520, arXiv.org, revised Mar 2023.
    3. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    4. Manesh, Sirous Fathi & Khaledi, Baha-Eldin & Dhaene, Jan, 2016. "Optimal allocation of policy deductibles for exchangeable risks," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 87-92.
    5. Martín Egozcue & Jiang Wu & Ričardas Zitikis, 2017. "Optimal two-stage pricing strategies from the seller’s perspective under the uncertainty of buyer’s decisions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    6. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    7. Deng Xiong & Liu Yanli, 2018. "A High-Moment Trapezoidal Fuzzy Random Portfolio Model with Background Risk," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 1-28, February.
    8. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    9. Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    10. Kaluszka, M. & Laeven, R.J.A. & Okolewski, A., 2012. "A note on weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 379-381.
    11. Choo, Weihao & de Jong, Piet, 2009. "Loss reserving using loss aversion functions," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 271-277, October.
    12. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    13. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    14. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.
    15. Furman, Edward & Kuznetsov, Alexey & Zitikis, Ričardas, 2018. "Weighted risk capital allocations in the presence of systematic risk," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 75-81.
    16. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.
    17. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2015. "A fuzzy portfolio selection model with background risk," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 505-513.
    18. Huang, Xiaoxia & Di, Hao, 2016. "Uncertain portfolio selection with background risk," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 284-296.

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