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Solvency Need Resulting from Reserving Risk in a ORSA Context

Author

Listed:
  • Geoffrey Nichil

    (Université de Lorraine)

  • Pierre Vallois

    (Université de Lorraine)

Abstract

The main goal of the paper is the evaluation of the Solvency Need SN(h), where h is the maximal duration of the insurance contracts that we will consider. We define it as the quantile of R(h, S) − 𝔼[R(h, S)], where R(h, S) is the reserve introduced in Nichil and Vallois (Insurance: Mathematics and Economics 66:29–43, 2016) and S := (Sx, x ⩾ 0) is a systemic risk. We prove that the normalized reserve converges in distribution, as h → + ∞, to the sum of a Gaussian RV and an independent RV which is an integral of a function of the systemic risk. In the case of mortgage guarantee we can go further in the description of the non-Gaussian RV and we propose three numerical schemes to estimate SN(h) when h is large and we compare the results of simulation.

Suggested Citation

  • Geoffrey Nichil & Pierre Vallois, 2019. "Solvency Need Resulting from Reserving Risk in a ORSA Context," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 567-592, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-017-9609-9
    DOI: 10.1007/s11009-017-9609-9
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    References listed on IDEAS

    as
    1. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Working Papers hal-00744351, HAL.
    2. Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Papers 1107.0164, arXiv.org, revised Apr 2012.
    3. Frédéric Planchet & Quentin Guibert & Marc Juillard, 2010. "Un cadre de référence pour un modèle interne partiel en assurance de personnes," Post-Print hal-00530864, HAL.
    4. Nichil, Geoffrey & Vallois, Pierre, 2016. "Provisioning against borrowers default risk," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 29-43.
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    6. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Papers 1210.6000, arXiv.org, revised Oct 2012.
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