Portfolio optimization in the case of an exponential utility function and in the presence of an illiquid asset
... is going to infinity. We show that the optimization problem with the exponential utility function is not connected to the optimization problem with the HARA utility by the limiting procedure and we obtain essentially different results. We provide the Lie group analysis of the corresponding HJB equation.
For the main three-dimensional PDE with the exponential utility function, we obtain the complete set of the nonequivalent Lie group invariant reductions to two-dimensional PDEs according to an optimal system ...