STOCHASTIC

ON OPTIMAL MYOPIC PORTFOLIO POLICIES 327
Case I.—(17) will first be replaced with
0 < z2j < mxj m > 1 j = 1, . . . , J - 1 , (18)
that is, 100/m is assumed to be the percentage margin requirement. The solution
to (10) for / — 1 now becomes
fj-\(Xj-i) =
zt.j-i(xj^) =
1/2[(1 - m)Xj^ + d]>" 0 < *,_, < d _
+ l/2[(2w + \)xj.,
2
+ i]"
lm i
Oj-ifj(xj-i) Xj-i > -z -r
ztn — l
«;-i 0 < Xj_i < ^ -
LW — 1
l/2(*j_, + d) *,_, > d ,
Lm — l
and the total solution is represented by (14)—(16) with bs > 0, j = 1, . . . , J — 1.
Consequently, the optimal portfolio policy is nonmyopic in the case of constraint
(18) also.
Case II.—Let us now introduce an absolute borrowing limit of m, that is, substitute
d
(19)
0 < zi, < x,•+ m m > 0 j = 1, . . . , J - 1 (20)
for (17). When m < d/2 the solution to (9) is again given by (14)—(16) with i> > 0,
j = 1, . . . , / — 1. However, when m > L = d/2, the solution becomes
/,(*,) = ai(xj +