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Variance Allocation and Shapley Value

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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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Authors and Affiliations

  1. Dipartimento di Economia e Finanza, LUISS, Viale Romania 32, 00197, Roma, Italy

    Riccardo Colini-Baldeschi & Marco Scarsini

  2. Dipartimento MEMOTEF, Sapienza-Università di Roma, Via Del Castro Laurenziano 9, 00161, Roma, Italy

    Stefano Vaccari

Authors
  1. Riccardo Colini-Baldeschi
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  2. Marco Scarsini
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  3. Stefano Vaccari
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Correspondence to Marco Scarsini.

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Riccardo Colini-Baldeschi is a member of is a member of GNCS-INdAM. Marco Scarsini is a member of GNAMPA-INdAM. His work is partially supported by PRIN 20103S5RN3 and MOE2013-T2-1-158.

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Colini-Baldeschi, R., Scarsini, M. & Vaccari, S. Variance Allocation and Shapley Value. Methodol Comput Appl Probab 20, 919–933 (2018). https://doi.org/10.1007/s11009-016-9540-5

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