Finance and Stochastics

, Volume 10, Issue 3, pp 341–352 | Cite as

Bounds for Functions of Dependent Risks

Original Paper


The problem of finding the best-possible lower bound on the distribution of a non-decreasing function of n dependent risks is solved when n=2 and a lower bound on the copula of the portfolio is provided. The problem gets much more complicated in arbitrary dimensions. When no information on the structure of dependence of the random vector is available, we provide a bound on the distribution function of the sum of risks which we prove to be better than the one generally used in the literature.


Copulas Dependent risks Dependence bounds Fréchet bounds 

Mathematics Subject Classifications (2000)

60E15 60E05 

JEL Classifications



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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Department of Mathematics for DecisionsUniversity of FirenzeFirenzeItaly

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