Collective risk-taking decisions with heterogeneous beliefs

Suppose that a group of agents having divergent expectations can share risks efficiently. We examine how this group should behave collectively to manage these risks. We show that the beliefs of the representative agent is in general a function of the group's wealth level, or equivalently, that the representative agent has a state-dependent utility function. We define the individual degree of pessimism as an index measuring probability differences across states. We show that the degree of pessimism of the representative agent is the mean of the individual ones weighted by their index of absolute risk tolerance. From this central result, we show how increasing disagreement on the state probability affects the state probability of the representative agent. We show that the divergence of opinions about the probability of occurrence of a boom may help solving the equity premium puzzle.