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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 maximiz- 
ation 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 pe- 
riod 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 re- 
garded as a separation of the decision problem in two suc- 
cessive 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