I think I can't get the idea of optimization based on utility. For some reasons, I should choose one of several common utility functions (exponential, isoelastic function and some others). Obviously, in it's formal representation as 1-exp(-a*Profit)- a (risk-aversion) doesn't make any sense in maximization. So, should any function be expanded by Taylor series, for example until 4th moment of distribution? Like this:
Would be glad if you could help me with this. I'm especially interested in isoelastic function. Thank you in advance!