TY - UNPB

T1 - Risk sharing under heterogeneous beliefs without convexity

AU - Liebrich, Felix-Benedikt

N1 - Minor changes in comparison to v1

PY - 2021/8/12

Y1 - 2021/8/12

N2 - 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 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.

AB - 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 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.

KW - q-fin.RM

KW - econ.GN

KW - q-fin.EC

KW - q-fin.MF

M3 - Preprint

BT - Risk sharing under heterogeneous beliefs without convexity

ER -