Utility function - risk averse?

[Outlaw]

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?

[NoMoreExams]

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?

[Outlaw]

Oops, Its from the textbook Bowers Actuarial Mathematics...

[NoMoreExams]

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.

[Outlaw]

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.

[BeanCounter]

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.