Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 919–933 | Cite as

Variance Allocation and Shapley Value

  • Riccardo Colini-Baldeschi
  • Marco ScarsiniEmail author
  • Stefano Vaccari


Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of n possibly dependent random variables. This criterion, the Shapley value, requires to translate the problem into a cooperative game. The Shapley value has nice properties, but, in general, is computationally demanding. The main result of this paper shows that in our particular case the Shapley value has a very simple form that can be easily computed. The same criterion is used also to allocate the standard deviation of the sum of n random variables and a conjecture about the relation of the values in the two games is formulated.


Shapley value Core Variance game Covariance matrix Computational complexity 

Mathematics Subject Classification (2010)

91A12 62J10 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Dipartimento di Economia e FinanzaLUISSRomaItaly
  2. 2.Dipartimento MEMOTEFSapienza-Università di RomaRomaItaly

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