There is a growing literature that studies the properties of models that combine
international trade and neoclassical growth theory, but mostly in a deterministic
setting. In this paper we introduce uncertainty in a dynamic
Heckscher-Ohlin model and characterize the equilibrium of a small open
economy in such an environment. We show that, when trade is balanced
period-by-period, the per capita output and consumption of a small open
economy converge to an invariant distribution that is independent of the initial
wealth. Further, at the invariant distribution, there are periods in which
the small economy diversifies. Numerical simulations show that the speed
of convergence increases with the size of the shocks. In the limit, when
there is no uncertainty, there is no convergence and countries may specialize
permanently. The paper highlights the role of market incompleteness, as a
result of the period-by-period trade balance, in this setup. Through an analytical
example we also illustrate the importance of country specific risk in
delivering our results.