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dramao
Topic Author
Posts: 1
Joined: March 25th, 2015, 1:20 am

### Textbook problem - Comparing Risk Aversion

I got stuck on this textbook problem.. On x>0, one von Neumann-Morgenstern utility function is given by x1-R, with 0<R<1, and another is given by x1-R + x1-Q, with 0<R<1 and 0<Q<1. In the sense of Arrow and Pratt, which is more risk averse and over what domain? Using the concept of strong risk aversion, is either more risk averse than the other for all x>0?Any idea how to solve it?I calculated the risk aversion for the utility functions respectively, but I can't compare the results.

kermittfrog
Posts: 63
Joined: September 9th, 2010, 10:25 am
Location: Frankfurt

### Textbook problem - Comparing Risk Aversion

Say A is the "only r" guy,B is the "r and q" guy, then - if I remember ocrrectly - A is more risk averse than B around x iff ARA_A(x) > ARA_B(x), where ARA is absolute level of risk aversion around x.Knowing that absolute risk aversion ARA(x) computes to -u''(x)/u'(x), we can write down both ARA:ARA_A>ARA_B-u_A''/u_A'>-u_B''/u_B'u_B'/u_A'>u_B''/u_A''...1>q/ri.e., B is more RA than A, iff q>r. Hope that helps.

ExSan
Posts: 4550
Joined: April 12th, 2003, 10:40 am

### Textbook problem - Comparing Risk Aversion

QuoteOriginally posted by: dramaoI got stuck on this textbook problem.. On x>0, one von Neumann-Morgenstern utility function is given by x1-R, with 0<R<1, and another is given by x1-R + x1-Q, with 0<R<1 and 0<Q<1. In the sense of Arrow and Pratt, which is more risk averse and over what domain? Using the concept of strong risk aversion, is either more risk averse than the other for all x>0?Any idea how to solve it?I calculated the risk aversion for the utility functions respectively, but I can't compare the results.which text book?