Explicit diversification benefit for dependent risks

Michel Dacorogna, Laila Elbahtouri and Marie Kratz ()
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Laila Elbahtouri: SCOR SE - SCOR SE [Paris]
Marie Kratz: ESSEC Business School

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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.

Keywords: Aggregation of risks; Archimedean copula; Clayton; Diversification (benefit); Gaussian; Gumbel; Heavy tail; Mixing technique; Pareto; Risk measure; TVaR; VaR; Weibull (search for similar items in EconPapers)
Date: 2015-12
New Economics Papers: this item is included in nep-ban and nep-rmg
Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01256869
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Working Paper: Explicit diversifiction benefit for dependent risks (2015)
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