Microsoft PowerPoint - PoF.ppt

ƒ 48

(Strict) risk aversion

ƒ

u’ > 0, (u’’ < 0) u’’

≤

0

... “(strictly) diminishing marginal utility“

ƒ

... “Jensen’s (strict) inequality”

ƒ

Certainty equivalent

(<)

≤

E[w]

ƒ

Risk premium

(>)

≥

0

ƒ

(strictly) risk averse iff

u

is (strictly) concave

ƒ

Risk neutral

ƒ

u ‘> 0, u’’ = 0

... “constant marginal utility”

ƒ ƒ

Certainty equivalent

= E[w]

ƒ

Risk premium

= 0

ƒ

risk neutral iff

u

is linear

(

)

[

]

(

)

[]

()

(

)

[

]

(

)

[

] w E u w u E w E u w u E

≤

<

(

)

[

]

(

)

[]

w E u w u E

=

Single-period random cashUtility functions: 3 (possible) categories

flows: Utility theory