AEB 6182 Lecture VII
Professor Charles Moss
1
Farm Portfolio Problem: Part III
Lecture VII
I.
Target Motad
A.
The target MOTAD model is a twoattribute risk and return model.
1.
Return is measured as the sum of the expected return of each activity
multiplied by the activity level.
2.
Risk is measured as the expected sum of the negative deviations of the
solution results from a targetreturn level.
3.
Risk is then varied parametrically so that a riskreturn frontier can be traced
out.
B.
Mathematically, the model is stated as
max
( )
x
j
j
j
n
ij
j
j
n
i
rj
j
j
n
r
r
r
r
n
E z
c x
st
a x
b
T
c x
y
p y
=
≤


≤
=
=
=
=
=
∑
∑
∑
∑
1
1
1
1
0
l
where:
1.
x
j
is the activity level for crop j.
2.
c
j
is the expected return on crop j.
3.
a
ij
is the technical coefficient in column I of row j.
4.
b
j
is the right hand side of that technical row.
5.
c
rj
is the r
th
outcome for activity j
6.
T is the target loss
7.
y
r
is the transfer of the negative deviation
8.
λ
is the target loss.
C.
The decision process can then be expressed as a locus of points where the whole
farm plan maximizes expected income subject to a target level of negative deviation.
II.
Discrete Sequential Stochastic Programming
A.
Target MOTAD, direct expected utility, and even MOTAD begin to develop the
concept of constraints being stochastic or met with some level of probability.
1.
In target MOTAD, income under a certain state exceeds the target level of
income with some probability.
2.
In direct expected utility maximization the level of wealth transferred to the
objective function was represented by a constraint which had some level of
probability.
3.
In MOTAD, we minimized the expected negative deviations which implied
stochastic constraints.
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Professor Charles Moss
2
4.
However, in each of these cases, the primary impact of stochastic
constraints was on the objective function or some threshold level of risk (as
was the case in target MOTAD).
B.
The variant of model that we want to develop is referred to as Discrete Sequential
Stochastic Programming (DSSP), although other names have been attributed to it.
This work grows out of work by Cocks, and focuses on decision processes which
are strung out over a discrete number of decision periods.
1.
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 Fall '08
 Moss
 Probability, Optimization, Utility, Probability theory, Professor Charles Moss

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