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Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation

Author

Listed:
  • Sarah Kaakai

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Anis Matoussi

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Achraf Tamtalini

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

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.

Suggested Citation

  • Sarah Kaakai & Anis Matoussi & Achraf Tamtalini, 2022. "Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation," Working Papers hal-03817818, HAL.
    • Handle: RePEc:hal:wpaper:hal-03817818
    Note: View the original document on HAL open archive server: https://hal.science/hal-03817818v2
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    References listed on IDEAS

    as
    1. Sarah Kaakai & Anis Matoussi & Achraf Tamtalini, 2022. "Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms," Papers 2211.16159, arXiv.org, revised Feb 2024.
    2. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2008. "Fast Simulation of Multifactor Portfolio Credit Risk," Operations Research, INFORMS, vol. 56(5), pages 1200-1217, October.
    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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    Keywords

    Multivariate risk measures; Optimized certainty equivalent; Numerical methods; stochastic algorithms; risk allocations;
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