Self-Enforcing Risksharing Arrangements in a Continuous-Time Endowment Economy

Résumé

We characterize efficient risksharing under two-sided limited commitment in a continuous-time endowment economy. Taking a dual approach based on the Lagrange multipliers on the participation constraints, we establish a strong duality result in a general setting. In a canonical application, agents have identical (time-separable, concave) preferences, aggregate endowment is constant, and endowment shares are driven by a mean-reverting diffusion process. The relevant co-state variable for the dual acts as a time-varying relative Pareto weight, which determines the static consumption allocation. We analyze the two-dimensional HJB equation associated with the (singular control) problem and solve for the free boundaries that delineate regions of the state space where participation constraints are binding. For some parameter values, perfect risksharing can be sustained despite limited commitment.