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.