A cooperative bargaining framework for decentralized portfolio optimization

Francisco Benita, Stefano Nasini and Rabia Nessah

Journal of Mathematical Economics, 2022, vol. 103, issue C

Abstract: Distributing a fixed budget among decentralized intermediaries is a relevant investment problem that has led to a growing research effort in the portfolio optimization literature. While existing contributions have widely focused on the incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has been generally overlooked. In this paper, we consider a cooperative bargaining game for the budget allocation in a class of decentralized investment problems, where financial intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. Focusing on the Nash bargaining solution and the Kalai–Smorodinsky bargaining solution, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation establishes a form of duality between a complex bilevel optimization model (resulting from the extensive formulation of the equilibrium conditions) and a convex knapsack problem. In the specific case of the Nash bargaining solution, the equilibrium characterization can be established as a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of quasi-homogeneity not only allows to numerically characterize a budget partitioning that balances fairness and efficiency in decentralized investment, but also gives rise to a computational approach that facilitates its numerical solvability.

Keywords: Cooperative bargaining; Portfolio optimization; Bilevel optimization; Knapsack problem (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:103:y:2022:i:c:s030440682200115x

DOI: 10.1016/j.jmateco.2022.102789

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