Bounds for Concave Distortion Risk Measures for Sums of Risks

Antonella Campana () and Paola Ferretti
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Antonella Campana: University of Molise

A chapter in Mathematical and Statistical Methods in Insurance and Finance, 2008, pp 43-51 from Springer

Abstract: Abstract In this paper we consider the problem of studying the gap between bounds of risk measures of sums of non-independentrandom variables. Owing to the choice of the context of where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure of a discrete risk by referring to its writing as sum of layers. Then, we examine the case of sums of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. Finally, the attention is devoted to the analysis of the gap between risk measures of upper and lower bounds, with the aim of optimizing it.

Keywords: Distortion risk measures; Discrete risks; Concave risk measures; Upper and lower bounds; Gap between bounds; 62H20; 60E15; D810 (search for similar items in EconPapers)
Date: 2008
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Working Paper: On Bounds for Concave Distortion Risk Measures for Sums of Risks (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-0704-8_6

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DOI: 10.1007/978-88-470-0704-8_6

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