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not easy to find this maximizing strategy, but it is very
simple when the preference function is quadratic and when
the constraints are linear. The solution is found by applying
the theorem of « first-period certainty equivalence », which
in our case amounts to the following: the first-period decision
of the maximizing strategy is identical with the first-period de:
cision that would be made if the uncertainty aspect would be
disregarded by replacing all random v’s by their expectations.
This means that the problem is reduced, for the decision of
the first year (x,) at least, to an ordinary conditional maximization
 problem: maximize the quadratic preference function
(not its expectation) subject to the constraint (3.4) on the
understanding that the vector s of this constraint is replaced by
its expectation; i.e., in (3.6) we should replace the v’s by the
expectations of the v’s. Clearly, this solves the uncertainty
problem in an almost trivial way. For the second-period de
cision (x,) one can proceed in precisely the same way one period
 later, because by that time the second period will have
become the first. And so on (3).

5. THE MAXIMIZING STRATEGY

The results mentioned in the preceding section can be regarded
 as a separation of the decision problem in two successive
 steps: first maximize as if there is no uncertainty,
then replace certain random variables in the result by their
expectations. We shall start with the first step under the
assumption that the horizon (T) is so large that it can be

(*) The first-period certainty equivalence theorem is due to H.A. St
MON [2] and was subsequently generalized by the present author [3, 4]
For applications to a microeconomic (paint factory) case reference is made
to C.C. Hort et alii [1]. For a more extensive discussion including several
other applications. see the author's recent monograph [5].

"71 Theil - pag. 11