Multiperiod Problems

Multiperiod problems consider the more general case where an investor makes a sequence of decisions, each possibly impacting the following ones. The objective is to find, at each period, the allocation decision that take into consideration a future changing opportunity set (i.e. availability of assets and their risk– return characteristics), the remaining investment horizon, eventual transaction costs, and other constraints such as the desire for intermediate consumption, minimization of tax impact, or the influx of additional capital due to labor income. These decisions, in general, are not identical to those obtained under the myopic (one-period) case, although they can be under specific assumptions (see §3.3/p. 48); more often, we shall see that the optimal solution is constructed from the myopic one as a starting point which is perturbed by a hedging demands term to account for “the future”. This term makes the obtained portfolio policies differ from iterated single-period ones.