A General Theory of Risk Sharing

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.