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Register a new userRisk sharing under heterogeneous beliefs without convexity
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Felix-Benedikt Liebrich
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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, individual risk assessments are assumed to be 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. Its proof combines local comonotone improvement with a Dieudonne-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.
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