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Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation

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  • Sarah Kaakai

    (LMM)

  • Anis Matoussi

    (LMM)

  • Achraf Tamtalini

    (LMM)

Abstract

We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as convexity, monotonocity and cash invariance. We also address numerical aspects of their computations using stochastic algorithms instead of using Monte Carlo or Fourier methods that do not provide any error of the estimation.

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  • Sarah Kaakai & Anis Matoussi & Achraf Tamtalini, 2022. "Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation," Papers 2210.13825, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2210.13825
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    References listed on IDEAS

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    1. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2008. "Fast Simulation of Multifactor Portfolio Credit Risk," Operations Research, INFORMS, vol. 56(5), pages 1200-1217, October.
    2. Sarah Kaakai & Anis Matoussi & Achraf Tamtalini, 2022. "Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms," Papers 2211.16159, arXiv.org, revised Feb 2024.
    3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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