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A General Theory of Risk Sharing

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  • Vasily Melnikov

Abstract

We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures. The existence of risk minimizing allocations is proved when constrained to satisfy economically convincing conditions. In the unconstrained case, we derive the dual representation of the value function using a Strassen-type theorem for the weak-star topology. These results are illustrated by explicit formulas when risk preferences are within the family of entropic and expected shortfall risk measures.

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  • Vasily Melnikov, 2025. "A General Theory of Risk Sharing," Papers 2505.19276, arXiv.org.
    • Handle: RePEc:arx:papers:2505.19276
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    References listed on IDEAS

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    1. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.
    2. Burgert, Christian & Rüschendorf, Ludger, 2008. "Allocation of risks and equilibrium in markets with finitely many traders," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 177-188, February.
    3. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
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