Rather than additional conditions on the first and second derivatives of u(x), other
contributions to the discussion of risk aversion add conditions that restrict the sign of
higher order derivatives of u(x). These conditions provide another way to strengthen
the requirement that A
u
(x) ≥ A
v
(x) for all x so that additional comparative static findings
can be obtained. Ekern (1980) does this in a very general fashion defining nth degree risk
aversion as follows.
Definition3.3:Decision maker with utility function u(x) is nth degree risk averse if
(−1)
n−1
· u
(n)
(x) > 0 for all x.
In this ...
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