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Conditional risk based on multivariate hazard scenarios

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Abstract

We present a novel methodology to compute conditional risk measures when the conditioning event depends on a number of random variables. Specifically, given a random vector \((\mathbf {X},Y)\), we consider risk measures that express the risk of Y given that \(\mathbf {X}\) assumes values in an extreme multidimensional region. In particular, the considered risky regions are related to the AND, OR, Kendall and Survival Kendall hazard scenarios that are commonly used in environmental literature. Several closed formulas are considered (especially in the AND and OR scenarios). An application to spatial risk analysis involving real data is discussed.

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Acknowledgements

We would like to thanks the Reviewers for helpful comments and careful reading. Helpful discussions with C. Sempi (Università del Salento, Lecce, Italy) are also gratefully acknowledged. [FD] This work was partially supported by the Faculty of Economics and Management, Free University of Bozen-Bolzano, via the project “NEW-DEMO”. Moreover, the work has been also partially supported by INdAM-GNAMPA Project 2017 “Bounds for Risk Functionals in Dependence Models”. [PJ] The support from National Science Centre, Poland, under project 2015/17/B/HS4/00911 is acknowledged. [GS] The support of the CMCC (Centro Euro-Mediterraneo sui Cambiamenti Climatici, Lecce (Italy)) is acknowledged.

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Authors and Affiliations

  1. Department of Statistical Sciences, University of Padua, Padua, Italy

    Mauro Bernardi

  2. Dipartimento di Scienze dell’Economia, Università del Salento, Lecce, Italy

    Fabrizio Durante

  3. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Piotr Jaworski

  4. Department MEMOTEF, Sapienza University of Rome, Rome, Italy

    Lea Petrella

  5. Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy

    Gianfausto Salvadori

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  1. Mauro Bernardi
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  2. Fabrizio Durante
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  3. Piotr Jaworski
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  4. Lea Petrella
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  5. Gianfausto Salvadori
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Correspondence to Fabrizio Durante.

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Bernardi, M., Durante, F., Jaworski, P. et al. Conditional risk based on multivariate hazard scenarios. Stoch Environ Res Risk Assess 32, 203–211 (2018). https://doi.org/10.1007/s00477-017-1425-9

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