[Sample B: Approval/Signature Sheet] - George Mason University

3.5 Attitude toward Risk
There are three possible attitudes toward risk that the DM can take: risk-averse,
risk-seeking and risk-neutral. To understand these concepts it is important to define
certainty equivalent (CE) and risk premium (RP).
First, consider a DM facing a lottery yielding either U$ 10,000 or U$ 2,000, with
equal probability of 0.5 for both outcomes. Clearly, the expected value (EV) of this
lottery is U$ 6,000. Suppose that the DM is asked to state his preference between
receiving U$6,000 for certain and taking the lottery. If he chooses to receive U$ 6,000 for
certain, it means that he prefers to avoid the risks associated with the lottery, thus
showing risk-aversion. The CE of this lottery would be the number such that the DM is
indifferent between the lottery and receiving a certain payoff.
In the example above, suppose that the DM is indifferent between receiving
U$ 4,000 (CE) and the lottery. The RP of this lottery is given by the expression
RP(L) = EV(L) – CE(L), where L is the associated lottery. This example would yield a
RP of U$ 2,000.
Thus, it is possible to state that, with respect to attitude toward risk, a DM is: 59
– Risk-averse if and only if for any nondegenerate lottery L, RP(L) > 0
– Risk-neutral if and only if for any nondegenerate lottery L, RP(L) = 0
– Risk-seeking if and only if for any nondegenerate lottery L, RP(L) < 0
59 Wayne L. Winston, Operations Research: Applications and Algorithms, 4th ed. (Duxbury Press, 2003),
750.
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