Portfolio turnpike theorems for constant policies

This paper develops general overtaking techniques for studying the asymptotic properties of portfolio policies optimal with respect to a terminal utility valuation. For a restricted class of utility functions the sequence of optimal constant (non-revised) portfolio policies formed as the horizon recedes into the future is shown to converge. Furthermore, for utility functions unbounded above and below, this turnpike policy need not be the policy associated with the minimal constant relative risk aversion function that bounds the valuation function from above. Finally, an analogy between the portfolio turnpike problem and the turnpike problem of growth theory is studied.