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Finance and Stochastics

, Volume 14, Issue 4, pp 593–623 | Cite as

On optimal portfolio diversification with respect to extreme risks

  • Georg Mainik
  • Ludger Rüschendorf
Article

Abstract

Extreme losses of portfolios with heavy-tailed components are studied in the framework of multivariate regular variation. Asymptotic distributions of extreme portfolio losses are characterized by a functional γ ξ =γ ξ (α,Ψ) of the tail index α, the spectral measure Ψ, and the vector ξ of portfolio weights. Existence, uniqueness, and location of the optimal portfolio are analysed and applied to the minimization of risk measures. It is shown that diversification effects are positive for α>1 and negative for α<1. Strong consistency and asymptotic normality are established for a semiparametric estimator of the mapping ξ γ ξ . Strong consistency is also established for the estimated optimal portfolio.

Keywords

Portfolio optimization Risk management Diversification effects Multivariate extremes 

Mathematics Subject Classification (2000)

62G32 62G05 62G20 62P05 

JEL Classification

C13 C14 G11 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematical StochasticsUniversity of FreiburgFreiburgGermany

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