Before revision:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity. In our previous papers devoted to the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure.
After revision:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to infinity. We show that the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure.