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Utility function - risk averse?

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  • Utility function - risk averse?

    How do you confirm that the utility function u(w) = log w, w > 0,
    is the utility function of a decision maker who is risk averse for w > 0?

    I came up with...
    u'(w) = 1/w ---------> Positive so w > 0
    u''(w) = -1/w^2 -------------> Negative so w < 0?
    So how to you confirm its risk averse for w > 0?

  • #2
    Originally posted by Outlaw View Post
    How do you confirm that the utility function u(w) = log w, w > 0,
    is the utility function of a decision maker who is risk averse for w > 0?

    I came up with...
    u'(w) = 1/w ---------> Positive so w > 0
    u''(w) = -1/w^2 -------------> Negative so w < 0?
    So how to you confirm its risk averse for w > 0?
    Since when did they add this to 1/P?

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    • #3
      Oops, Its from the textbook Bowers Actuarial Mathematics...

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      • #4
        Originally posted by Outlaw View Post
        Oops, Its from the textbook Bowers Actuarial Mathematics...
        That textbook is 3/MLC though when I passed that exam, utility functions weren't on there. They did change the syllabus however so it's possible they added it.

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        • #5
          Oh ok, I don't plan on taking any Actuarial exam though, just took a Actuarial math class at my college to get a feel of Actuarial Math. Thanks for the reply.

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          • #6
            You can also find this function from one of the SOA recommended Exam P textbook, Probability for Risk Management. However, it is not required for Exam P.

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