Arrow-Pratt Coefficient of Risk Aversion:

The measure of absolute risk aversion is given by  

the following three statements are equivalent

With the above conditions, it will  be  possible for you to conclude that individual with vNM within function  u is more risk averse than the one with vNM utility function w.

You  should keep in mind  that this  is  only  an  incomplete  ranking and it  is possible that  you  can't compare  two risk-averse  individuals  in  this  way. However, within an important subclass of utility functions, known as constant absolute risk-aversion (CARA)  utility  functions, the  ranking  is  complete. These are the utility functions of the form

for these, the coefficient of absolute risk-aversion

There is a problem with CARA utility functions, however.absolute  risk-averse individuals are concerned only with absolute  size of the risk they are exposed to. Whether a possible loss of Rs. 1000 represents .5%, 5%. or 50% of her net worth, an individual with CARA preferences will view  it in the same manner. Therefore, it may be useful to  consider the Arrow-Pratt coefficient of relative risk-aversion, which can be written as

This formulation focuses on the size of the gamble as a proportion of one's wealth  and constant relative  risk-aversion  implies decreasing absolute risk- aversion.

You will be dealing, mostly, with the constant relative risk-aversion (CRRA) utility functions of the form,