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- W3217761483 abstract "We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations with self-regulation in the special case where the interaction matrix is of unit rank, corresponding to species competing for a common resource. We compute the average number of solutions and show that its logarithm grows as $N^alpha$, where $N$ is the number of assets or species and $alpha leq 2/3$ depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity $m(N)$ of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, ``disorder chaos'' is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number ``satisficing'' solutions." @default.
- W3217761483 created "2021-12-06" @default.
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- W3217761483 date "2021-01-01" @default.
- W3217761483 modified "2023-09-26" @default.
- W3217761483 title "A New Spin on Optimal Portfolios and Ecological Equilibria" @default.
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- W3217761483 doi "https://doi.org/10.2139/ssrn.3817718" @default.
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