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Risk sharing under heterogeneous beliefs without convexity

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  • Felix-Benedikt Liebrich

Abstract

We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations. We do not assume their convexity though. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotone improvement with a Dieudonn\'e-type argument, which also establishes a link of the optimal allocation problem to the realm of "collapse to the mean" results. Finally, we extend the results to capital requirements with multidimensional security markets.

Suggested Citation

  • Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2108.05791
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    References listed on IDEAS

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    1. Moresco, Marlon Ruoso & Righi, Marcelo Brutti, 2022. "On the link between monetary and star-shaped risk measures," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Marcelo Brutti Righi, 2021. "Star-shaped acceptability indexes," Papers 2110.08630, arXiv.org, revised Jun 2022.

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