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.
CITATION STYLE
Colini-Baldeschi, R., Scarsini, M., & Vaccari, S. (2018). Variance Allocation and Shapley Value. Methodology and Computing in Applied Probability, 20(3), 919–933. https://doi.org/10.1007/s11009-016-9540-5
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