Collective completeness and pricing-hedging duality II

Battle Count: 79

The paper provides foundational theoretical results for multi-agent asset pricing and risk sharing. While not directly producing trading signals or algorithms, it establishes the mathematical framework for understanding when collective hedging strategies are viable, how pricing bounds behave under directional exchange constraints, and when market completeness holds in cooperative settings. Relevant for institutional risk managers designing inter-entity risk transfer agreements and for understanding the limits of cooperation in segmented markets. The cone-valued exchange framework is particularly relevant for modeling insurance-like risk transfers and regulatory constraints on inter-entity exposures.

This is a pure mathematical theory paper requiring advanced knowledge of functional analysis, convex analysis, measure theory, and stochastic processes. There are no algorithms to implement. The mathematical machinery (Hilbert space projections, Kreps-Yan separation, polyhedral cone theory, Radon-Nikodym derivatives) is highly abstract. Practical implementation would require significant adaptation to specific market models. The finite-state examples in Section 4 are computationally tractable but illustrative only.

As a pure mathematical theory paper, all results are fully specified with complete proofs. The discrete-time finite-state examples (Section 4) are explicitly constructed and verifiable. No computational experiments are needed. The main limitation is the high mathematical sophistication required to verify proofs. No code or datasets are provided or needed.