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Risk measurement in the presence of background risk

Tsanakas, A. (2008). Risk measurement in the presence of background risk. Insurance: Mathematics and Economics, 42(2), pp. 520-528. doi: 10.1016/j.insmatheco.2007.01.015


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.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Insurance: Mathematics and Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics and Economics, Volume 42, Issue 2, April 2008, Pages 520–528,
Publisher Keywords: Risk measures; Background risk; Capital allocation; Portfolio management; Elliptical distributions
Subjects: H Social Sciences > HF Commerce
Departments: Bayes Business School > Actuarial Science & Insurance
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