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Consider a portfolio problem
with investments held over a period of time. Let denote
the amount of investment throughout the period with a unit
total budget, i.e.,
and let denote the price change of
investment over the period. Then, the overall expected return
is given by Furthermore, let
denote the
covariance between the returns for investment and The
variance of the return is
referred to the risk.
Here we consider that the
are fixed and computed
from historical data. A similar application can also be found in
[15].
One approach is to minimize the risk over the return with a lower
bound ,

(37) 
Another approach is to maximize the return over the risk with an
upper bound

(38) 
The above models are based on historical data.
Example 4. Two test cases from (37) and
(38) are cast as in formula (11) with the real
data from optrisk.mod in [16]. Another case which combines
(37) and (38),
is also considered.
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Up: Application Problems
Previous: Facility Location Problem (II)
Hans D. Mittelmann
20030910