The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain Pareto optimal allocations. We consider an in…nite horizon stochastic endowment economy where the actual process of the states of nature consists in i.i.d draws from a common probability distribution. The economy is populated by many Bayesian agents with heterogeneous prior beliefs over the stochastic process of the states of nature. Since Pareto optimal allocations are typically history dependent, we propose a method to provide a complete recursive characterization when agents know the likelihood function generating the data but have di¤erent beliefs about the probability distribution of these draws. Under these assumptions, we show that if every agent’s belief contains the true probability distribution of the states of nature, then investors’equilibrium asset holdings converge with probability one and, consequently, any genuine asset trading vanishes with probability one. Finally, we provide examples in which asset trading does not vanish asymptotically because either (i) no agent has the true probability distribution of the states of nature in the support of her prior belief or (ii) agents disagree on the likelihood function that generates the data.