A Case Study in Multiperiod Portfolio Optimization: A Classic Problem Revisited

Conventional wisdom holds that multiperiod portfolio optimization problems are best, if not only, solved by dynamic programming. But dynamic programming suffers from the curse of dimensionality whereby optimization becomes intractable as time horizon and number of assets increase, thereby limiting its practical applications. In this paper I show for a classic multiperiod investment problem that a feed-forward, open-loop procedure, amenable to solution by conventional methods (e.g. calculus of variations) and not subject to the curse of dimensionality, generates `here and now' portfolios identical to those generated by the dynamic programming approach. The analytic results in this paper demonstrate that for this classic problem a feed forward approach is not inferior to the more common backward induction approach, suggesting that an `open-loop with recourse' process is a viable closed-loop approach for some practically useful multiperiod investment problems.