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Bounds for Concave Distortion Risk Measures for Sums of Risks

In: Mathematical and Statistical Methods in Insurance and Finance

Author

Listed:
  • Antonella Campana

    (University of Molise)

  • Paola Ferretti

    (University of Venice)

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.

Suggested Citation

  • Antonella Campana & Paola Ferretti, 2008. "Bounds for Concave Distortion Risk Measures for Sums of Risks," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 43-51, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-0704-8_6
    DOI: 10.1007/978-88-470-0704-8_6
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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