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Surplus-invariant risk measures

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  • Niushan Gao
  • Cosimo Munari

Abstract

This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper we develop a theory of surplus invariance in its natural framework, namely that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural results for surplus-invariant acceptance sets. We illustrate the power of the lattice approach by specifying our results to model spaces with a dominating probability, including Orlicz spaces, as well as to robust model spaces without a dominating probability, where the standard topological techniques and exhaustion arguments cannot be applied.

Suggested Citation

  • Niushan Gao & Cosimo Munari, 2017. "Surplus-invariant risk measures," Papers 1707.04949, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1707.04949
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    References listed on IDEAS

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    1. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.
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    6. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    7. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
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    Cited by:

    1. Chen, Ouxiang & Hu, Taizhong, 2019. "Extreme-aggregation measures in the RDEU model," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 155-163.

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