Article ID: | iaor2005731 |
Country: | Netherlands |
Volume: | 122 |
Issue: | 3 |
Start Page Number: | 573 |
End Page Number: | 597 |
Publication Date: | Sep 2004 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Pang T. |
Keywords: | portfolio selection |
A portfolio optimization problem on an infinite-time horizon is considered. Risky asset prices obey a logarithmic Brownian motion and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite-horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. The problem is then reduced to a one-dimensional stochastic control problem by virtue of the Girsanov transformation. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The subsolution/supersolution method is used to obtain existence of solutions of the DPE. The solutions are then used to derive the optimal investment and consumption policies. In addition, for a special case, we obtain the results using the viscosity solution method.