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On Coherency and Other Properties of MAXVAR

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Abstract

This paper is concerned with the MAXVAR risk measure on \(\mathscr {L}^{2}\) space. We present an elementary and direct proof of its coherency and averseness. Based on the observation that the MAXVAR measure is a continuous convex combination of the CVaR measure, we provide an explicit formula for the risk envelope of MAXVAR.

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Acknowledgements

We would like to thank the anonymous referees for their useful suggestions, which are of great help for improving the manuscript.

Funding

The research of Jie Sun is partially supported by the Australian Research Council under Grant DP160102819. The research of Qiang Yao is partially supported by grants from the National Science Foundation of China (Nos.11201150 and 11126236) and the 111 Project (No. B14019).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, People’s Republic of China

    Jie Sun

  2. School of Science and CIC, Curtin University, Perth, Australia

    Jie Sun

  3. School of Statistics, East China Normal University, Shanghai, People’s Republic of China

    Qiang Yao

  4. NYU—ECNU Institute of Mathematical Sciences, NYU Shanghai, Shanghai, People’s Republic of China

    Qiang Yao

Authors
  1. Jie Sun
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  2. Qiang Yao
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Corresponding author

Correspondence to Jie Sun.

Additional information

This paper is dedicated to Michel Théra in celebration of his 70th birthday.

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Sun, J., Yao, Q. On Coherency and Other Properties of MAXVAR. Vietnam J. Math. 46, 87–94 (2018). https://doi.org/10.1007/s10013-017-0262-y

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  • DOI: https://doi.org/10.1007/s10013-017-0262-y

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