A degenerate elliptic equation arising in an optimization problem under partial information

Abstract

In a financial market where risky securities are affected by hidden economic factors, we consider an optimal consumption/investment problem for the expected HARA utility of the investor's wealth on infinite time horizon. We report some results on the related Hamilton-Jacobi-Bellman equation, which is, after some transformation, a second order linear degenerate elliptic equation. Using its solution, an optimal consumption/investment strategy is specified.