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Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms

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

Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating MSRM and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples.

Suggested Citation

  • Sarah Kaakai & Anis Matoussi & Achraf Tamtalini, 2024. "Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms," Working Papers hal-03871246, HAL.
    • Handle: RePEc:hal:wpaper:hal-03871246
    Note: View the original document on HAL open archive server: https://hal.science/hal-03871246v3
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    More about this item

    Keywords

    Multivariate risk measures; shortfall risk; stochastic algorithms; stochastic root finding; risk allocations;
    All these keywords.

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