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Some multivariate risk indicators: Minimization by using a Kiefer–Wolfowitz approach to the mirror stochastic algorithm

Author

Listed:
  • Cénac P.
  • Maume-Deschamps V.

    (Universit´e Lyon 1, Laboratoire SAF EA 2429, LYON CEDEX 7, Frankreich)

  • Prieur C.

    (Universite Joseph Fourier, Tour IRMA, MOISE-LJK, Grenoble Cedex 9, Frankreich)

Abstract

We consider some risk indicators of vectorial risk processes. These indicators take into account the dependencies between business lines as well as some temporal dependencies. By using stochastic algorithms, we may estimate the minimum of these risk indicators, under a fixed total capital constraint. This minimization may apply to capital reserve allocation.

Suggested Citation

  • Cénac P. & Maume-Deschamps V. & Prieur C., 2012. "Some multivariate risk indicators: Minimization by using a Kiefer–Wolfowitz approach to the mirror stochastic algorithm," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 47-72, March.
    • Handle: RePEc:bpj:strimo:v:29:y:2012:i:1:p:47-72:n:2
    DOI: 10.1524/strm.2012.1069
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    References listed on IDEAS

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    1. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.
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    3. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes and optimal reserve allocation," Post-Print hal-00397289, HAL.
    4. Lelong, Jérôme, 2008. "Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2632-2636, November.
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    6. Picard, Philippe, 1994. "On some measures of the severity of ruin in the classical Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 107-115, May.
    7. Stéphane Loisel, 2005. "Differentiation of some functionals of multidimensional risk processes and determination of optimal reserve allocation," Post-Print hal-00397287, HAL.
    8. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
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