Nash Bargaining Partitioning in Decentralized Portfolio Management

In the context of decentralized portfolio management, understanding how to distribute a fixed budget among decentralized intermediaries is a relevant question for financial investors. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. We propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures) and allows the reduction of a complex bilevel optimization model to a convex separable knapsack problem. As numerically shown using stock returns data from U.S. listed enterprises, this modelling reduction of the Nash bargaining solution in decentralized investment (driven by the notion of quasi-homogeneous measures), allows solving the vast majority of large-scale investment instances in less than a minute.



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