STOCHASTIC

OPTIMAL INVESTMENT 589
M: the number of available investment opportunities.
S: the subset of investment opportunities which it is possible to sell short.
ztj: amount invested in opportunity i, i = 1,...,M, at the beginning of the7th period (decision
variable).
r - 1: rate of interest, where r > 1.
Pt: transformation of each unit of capital invested in opportunity i in any period j (random variable);
that is, if we invest an amount 0 in i at the beginning of a period, we will obtain ftO at the end of that period
(stochastically constant returns to scale, no transaction costs or taxes). The joint distribution functions
of the fa, i = 1,..., M, are assumed to be known and independent with respect to time). The {ft} have
the following properties:
P) 0, = r,
(3) 0€ft