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On Debreu-Koopmans Theorem for Additively Decomposed Quas...
[Submitted on 17 Mar 2026 (v1), last revised 2 Jun 2026 (this ve · 2026-06-03 · via math updates on arXiv.org

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Abstract:The Debreu Koopmans theorem restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable, additive or multiplicative, function is star quasiconvex, those with star shaped sublevel sets about minimizers, if and only if each component is star quasiconvex. This immediately yields star quasiconvexity of separable sums of quasiconvex functions, formally bridging diversification theory with the S shaped value functions of Prospect Theory. Furthermore, we develop a complete calculus, monotonic composition, pointwise minima, quasi arithmetic means, and we apply it to Cobb-Douglas functions, multifactor risk models, and constant function market makers in decentralized finance. Star quasiconvexity thus provides a unified framework for applications in optimization and economic modeling beyond the classical Debreu Koopmans constraint. The introduction discuss economic motivations.

Submission history

From: Felipe Lara [view email]
[v1] Tue, 17 Mar 2026 19:17:55 UTC (286 KB)
[v2] Tue, 2 Jun 2026 03:15:19 UTC (286 KB)