Explicit diversifiction benefit for dependent risks

Michel Dacorogna, Laila Elbahtouri and Marie Kratz ()
Additional contact information
Laila Elbahtouri: SCOR
Marie Kratz: Essec Business School

No WP1522, ESSEC Working Papers from ESSEC Research Center, 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.

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)
Pages: 22 pages
Date: 2015-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://hal-essec.archives-ouvertes.fr/hal-01256869/document (application/pdf)

Related works:
Working Paper: Explicit diversification benefit for dependent risks (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ebg:essewp:dr-15022

Access Statistics for this paper

More papers in ESSEC Working Papers from ESSEC Research Center, ESSEC Business School ESSEC Research Center, BP 105, 95021 Cergy, France. Contact information at EDIRC.
Bibliographic data for series maintained by Sophie Magnanou ().