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Systemic Risk: Conditional Distortion Risk Measures

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  • Jan Dhaene
  • Roger J. A. Laeven
  • Yiying Zhang

Abstract

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and risk contribution measures in terms of the VaR and ES as special cases. Sufficient conditions are presented for two random vectors to be ordered by the proposed CoD-risk measures and distortion risk contribution measures. These conditions are expressed using the conventional stochastic dominance, increasing convex/concave, dispersive, and excess wealth orders of the marginals and canonical positive/negative stochastic dependence notions. Numerical examples are provided to illustrate our theoretical findings. This paper is the second in a triplet of papers on systemic risk by the same authors. In \cite{DLZorder2018a}, we introduce and analyze some new stochastic orders related to systemic risk. In a third (forthcoming) paper, we attribute systemic risk to the different participants in a given risky environment.

Suggested Citation

  • Jan Dhaene & Roger J. A. Laeven & Yiying Zhang, 2019. "Systemic Risk: Conditional Distortion Risk Measures," Papers 1901.04689, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1901.04689
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    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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