Thursday, September 6, 2012

Question from Tracey

Tracey asked:

Hi Professor Arvan,
I have viewed some of your video's on YouTube, and was wondering if you provide people with the Excel spreedsheet's? I am particularly interested in having a closer look at the one you used for the Expected Utility Hypothesis video.
All the spreadsheets can be found here.  Each of the workbooks there must be downloaded and used in Excel.  There are multiple spreadsheets per workbook.  The name of the spreadsheet should coincide with the name of the video.

Question from Mark

Mark asked:

First off, thanks for your videos. They help.My question:Assuming I have 0 means lottery X, (-6 with 1/2 probability and 6 with 1/2 probability) and utility function u(w)=w for w<=10 and u(w)=1/2w+5 for w>=10
Can I apply the Arrow-Pratt approximation of pi(w;X)=1/2 (sigma)^2A(w)?
My hunch is no since A(w)=0 in either case of u(w)...i think?? My question is what does A(w)=0 mean? and why does Arrow-Pratt not work here?

My response - The Arrow-Pratt Measure applies to utility functions that are twice differentiable.  In the example above the utility function is piece-wise linear, with a kink at 10.   It is not differentiable at the kink, so it is outside the class of functions for which the measure is intended.  Alternatively, if you prefer, when w is not 10, the individual is risk neutral (for small gambles).  When w is 10, the individual is infinitely risk averse.