Lecture03-1996 - Lecture III Specific Arrow-Pratt Orange...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Lecture III: Specific Arrow-Pratt, Orange Tree Example, Stochastic Dominance, Beginning Mean-Variance I. An examination of the Arrow-Pratt Coefficients for particular functions. A. Quadratic Utility Function: To specify the appropriate shape of the utility function, the quadratic function becomes ( ) ( ) ( ) 2 2 2 U w aw bw U w a bw U w b = = ′′ = − Arrow-Pratt absolute risk aversion coefficient: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 1 2 0 2 A A A b b R w R w a bw a bw d R w f x b d b dw dx f x a bw f x = − = = > = − Arrow-Pratt relative risk aversion coefficient ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 0 2 2 R R b b R w w a a bw b w d R w b b b dw a bw a bw = = = + > B. Power Utility Function: ( ) ( ) ( ) 1 1 1 r r r w U w r U w w U w rw − − = = ′′ = − Arrow-Pratt absolute risk aversion coefficient: ( ) ( ) 1 2 0 r A r A rw r R w w w d R w r dw w − − = − = = − < Arrow-Pratt relative risk aversion coefficient: ( ) ( ) 1 0 r R r R rw w R w r w d R w dw − − = − = = Constant relative risk aversion. C. Negative Exponential Utility Function:
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 ( ) ( ) ( ) ( ) ( ) ( ) 2 exp exp exp U w w U w w U w w = − −ρ = ρ −ρ ′′ = ρ −ρ Arrow-Pratt absolute risk aversion coefficient ( ) ( ) ( ) ( ) 2 exp exp 0 A A w R w w d R w dw −ρ −ρ = − = ρ ρ −ρ = Constant absolute risk aversion. Arrow-Pratt relative risk aversion coefficient ( ) ( ) ( ) ( ) 2 exp exp 0 R R w R w w w w d R w dw −ρ −ρ = − = ρ ρ −ρ = ρ > D. HARA–Hyperbolic Absolute Risk Aversion: ( ) ( ) ( ) ( ) ( ) 1 1 2 2 2 1 , 0 1 1 1 1 1 1 1 1 1 aw U w b b aw a U w b aw a b aw a U w a b aw a b γ γ− γ− γ− γ− − γ = + > γ − γ = − γ + − γ − γ = + − γ ′′ = γ − +
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern