Optimal Investment Policy on Consumption and Portfolio Problem for Companies with Debts

We consider a class of optimal consumption and portfolio problem that a corporation faces in which it must pay some debt liability continuously at a given rate due to a previous debt financing, such as bond liability or loan amortization. We model the dynamics of the corporate assets as a diffusion process with controlled drift. In this problem, what the corporation mostly concerns about is how to attain the previously fixed objective assets level in the shortest time, i.e. the objective of the management is to choose the fraction of the total assets invested in the risky asset to minimize the expected time that the corporation first get the previously fixed objective assets. With Bellman dynamic programming principle we find the corresponding optimal policy and the corresponding optimal expected time. We also give some numerical cases for the problem.