The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynam-ically complete markets equilibria when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates contin-uous trade and signi\u85cant uctuations in individual portfolios may be correct but it also needs some quali\u85cations. We consider an in\u85nite horizon stochastic endowment economy where the actual process of the states of nature consists in i.i.d. draws. The economy is populated by many Bayesian agents with hetero-geneous priors over the stochastic process of the states of nature. Our approach hinges on studying portfolios that support Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents know that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed gen-erate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the support of every agents prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d