Microsoft PowerPoint - PoF.ppt

Some utility functionsƒ 50

Power utility

ƒ

Quadratic utility (special case of power utility: for

N

= -1

)

ƒ

Negative exponential utility

ƒ

Logarithmic utility

ƒ

All these utility functions are strictly increasing and strictly concave!

()

w

A

w

for

w

w

u

+ = < − + =

α

α

α

1

,

,

ln

)

(

α

α

α

=

>

−

=

−

A

for

e

w

u

w

,

0

,

)

(

()

w

A

w

for

w

w

u

− = < − − =

α

α

α

1

,

,

1 2

)

(

2

()

w

A

and

w

for

w

w

u

γ α γ γ γ α γ α γ

γ

+ = ≠ ≠ < − + − =

−

1

, 1

, 0 , , 1 1 ) (

1

1

Single-period random cash

flows: Utility theory