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Vector Risk Functions

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Abstract

The paper introduces a new notion of vector-valued risk function, a crucial notion in Actuarial and Financial Mathematics. Both deviations and expectation bounded or coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding points of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems and practical examples are provided.

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Authors and Affiliations

  1. University Carlos III of Madrid, CL. Madrid 126, 28903, Getafe, (Madrid), Spain

    Alejandro Balbás

  2. Department of Actuarial and Financial Economics, University Complutense of Madrid, Somosaguas Campus, 28223, Pozuelo de Alarcón, (Madrid), Spain

    Raquel Balbás

  3. Department of Fundamental Mathematics, Spanish Open University, CL. Senda del Rey, 9, 28040, Madrid, Spain

    Pedro Jiménez-Guerra

Authors
  1. Alejandro Balbás
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  2. Raquel Balbás
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  3. Pedro Jiménez-Guerra
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Corresponding author

Correspondence to Pedro Jiménez-Guerra.

Additional information

The authors thank Professor C. Zalinescu and the anonymous reviewer for their useful comments and suggestions. This research was partially supported by “Comunidad Autónoma de Madrid” (Spain), Grant S2009ESP − 1685, and “Ministerio de Ciencia en Innovación” (Spain), Grant ECO2009 − 14457 − C04. The usual caveat applies.

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Balbás, A., Balbás, R. & Jiménez-Guerra, P. Vector Risk Functions. Mediterr. J. Math. 9, 563–574 (2012). https://doi.org/10.1007/s00009-011-0153-5

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  • DOI: https://doi.org/10.1007/s00009-011-0153-5

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