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Adjusted Expected Shortfall

Author

Listed:
  • Matteo Burzoni

    (Università degli studi di Milano - Dipartimento di Matematica)

  • Cosimo Munari

    (University of Zurich - Department of Banking and Finance; Swiss Finance Institute)

  • Ruodu Wang

    (University of Waterloo - Department of Statistics and Actuarial Science)

Abstract

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum amount of capital that has to be raised and injected into a financial position X to ensure that Expected Shortfall ESp(X) does not exceed a pre-specified threshold g(p) for every probability level p\in[0,1]. Through the choice of the benchmark risk profile g one can tailor the risk assessment to the specific application of interest. We devote special attention to the study of risk profiles defined by the Expected Shortfall of a benchmark random loss, in which case our risk measures are intimately linked to second-order stochastic dominance.

Suggested Citation

  • Matteo Burzoni & Cosimo Munari & Ruodu Wang, 2020. "Adjusted Expected Shortfall," Swiss Finance Institute Research Paper Series 20-120, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp20120
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    More about this item

    Keywords

    Convex Risk Measures; Tail Risk; Adjusted Expected Shortfall; Stochastic Dominance; Capital Adequacy; Optimization With Risk Measures;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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