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Utility functions: degree of risk aversion 49

u

is unique up to a strictly increasi

ng affine transformation (, i.e.

u

can

be replaced by

a+bu

for any constants

a

and

b

>0 without changing the

preference ordering of

u

)

Ä

such a transformation should not change

the measure of risk aversion! Ä

Arrow-Pratt measure of absolute risk aversion Ä

Risk tolerance Ä

Arrow-Pratt measure of relative risk aversion

'' ' u u

A

− =

A

T

1 =

'' '

*

u u w

A

w

R

− =

=

Single-period random cash

flows: Utility theory