Risk Sharing with Higher Dimensional Security Spaces

We discuss the risk sharing problem in a Riesz space economy where the commodities are aggregated financial losses a system of finitely many agents may incur. We analyse the problem using a notion of risk measurement which... [ view full abstract ]

We discuss the risk sharing problem in a Riesz space economy where the commodities are aggregated financial losses a system of finitely many agents may incur. We analyse the problem using a notion of risk measurement which extends the classical cash-additive case and prove the existence of Pareto optimal and equilibrium allocations for polyhedral agent systems and law-invariant acceptance criteria. Moreover, we will present results on continuity properties of set-valued maps mapping an aggregated initial loss or a loss endowment to its optimal allocations.