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Explicit diversification benefit for dependent risks

Author

Listed:
  • Michel Dacorogna

    (SCOR SE - SCOR SE [Paris])

  • Laila Elbahtouri

    (SCOR SE - SCOR SE [Paris])

  • Marie Kratz

    (ESSEC Business School)

Abstract

We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.

Suggested Citation

  • Michel Dacorogna & Laila Elbahtouri & Marie Kratz, 2015. "Explicit diversification benefit for dependent risks," Working Papers hal-01256869, HAL.
    • Handle: RePEc:hal:wpaper:hal-01256869
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01256869
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    References listed on IDEAS

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    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
    2. Groenendijk, Patrick A. & Lucas, André & Vries, Casper G. de, 1997. "Stochastic processes, non-normal innovations, and the use of scaling ratios," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
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    Cited by:

    1. Cuberos A. & Masiello E. & Maume-Deschamps V., 2015. "High level quantile approximations of sums of risks," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, October.

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    More about this item

    Keywords

    Aggregation of risks; Archimedean copula; Clayton; Diversification (benefit); Gaussian; Gumbel; Heavy tail; Mixing technique; Pareto; Risk measure; TVaR; VaR; Weibull;
    All these keywords.

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