Investment and bilateral insurance

Private information may limit insurance possibilities when two agents get together to pool idiosyncratic risk. However, if there is capital accumulation, bilateral insurance possibilities may improve because misreporting distorts investment. We show that if one of the Pareto weights is sufficiently large, that agent does not have incentives to misreport. This implies that, under some conditions, the full information allocation is incentive compatible when agents have equal Pareto weights. In the long run, either one of the agents goes to immiseration, or both agents' lifetime utilities are approximately equal. The second case is only possible with capital accumulation.