Variance Allocation and Shapley Value

Riccardo Colini-Baldeschi; Marco Scarsini; Stefano Vaccari

doi:10.1007/s11009-016-9540-5

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arXiv · 1606.09424

Variance Allocation and Shapley Value

Riccardo Colini-Baldeschi·Marco Scarsini·Stefano Vaccari

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Abstract

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.

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BibTeX RIS

Riccardo Colini-Baldeschi, Marco Scarsini, Stefano Vaccari. 2017-01-01. Variance Allocation and Shapley Value. https://doi.org/10.1007/s11009-016-9540-5

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