Segmented Risk-Sharing in a Continuous Time Setting

In an economy with a continuum of individuals, each individual has a stochastic, continuously evolving endowment process. Individuals are risk averse and would therefore like to insure their endowment processes. It is feasible to obtain insurance by pooling endowments across individuals because the processes are mutually independent. We characterize the payoff from an insurance contracting scheme of this type, and we investigate whether such scheme would survive as an equilibrium in a noncooperative setting.