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.

Variance Allocation and Shapley Value / COLINI BALDESCHI, Riccardo; Scarsini, Marco; Vaccari, Stefano. - In: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY. - ISSN 1387-5841. - 20:3(2018), pp. 919-933. [10.1007/s11009-016-9540-5]

Variance Allocation and Shapley Value

COLINI BALDESCHI, RICCARDO;SCARSINI, MARCO;VACCARI, STEFANO
2018

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.
Shapley value, Core, Variance game, Covariance matrix, Computational complexity
Variance Allocation and Shapley Value / COLINI BALDESCHI, Riccardo; Scarsini, Marco; Vaccari, Stefano. - In: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY. - ISSN 1387-5841. - 20:3(2018), pp. 919-933. [10.1007/s11009-016-9540-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/172054
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