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Quasiconvex risk statistics with scenario analysis

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Abstract

We introduce the definitions of quasiconvex risk statistics. Using dual method, we provide representation results for comonotonic quasiconvex risk statistics and empirical-law-invariant quasiconvex risk statistics. In particular, we present some specific examples related to certainty equivalence and Basel margin requirement.

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Notes

  1. Comonotonic subadditive (resp. comonotonic convex) risk measures preserving SSD are equivalent to coherent (resp. convex) risk measures preserving SSD under some milder condition. Therefore, some representation results have been already obtained in Dana [6] or Leitner [15].

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Acknowledgments

The authors would like to thank the Co-Editor and an anonymous reviewer for their insightful comments and valuable suggestions, which have helped us to improve the paper. This work was supported by NSFC (11371362, 11101422) and the Fundamental Research Funds for the Central Universities (2012LWB17).

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  1. School of Sciences, China University of Mining and Technology, Xuzhou, 221116, China

    Dejian Tian & Long Jiang

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  1. Dejian Tian
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  2. Long Jiang
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Correspondence to Dejian Tian.

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Tian, D., Jiang, L. Quasiconvex risk statistics with scenario analysis. Math Finan Econ 9, 111–121 (2015). https://doi.org/10.1007/s11579-014-0136-y

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