Optimal investment with a corporate bond

The present paper analyzes the optimal investment strategy in a corporate (defaultable) bond, a stock and a bank account in a continuous time model. We model the corporate bond price through a reduced-form approach and solve the dynamics of its price. The optimal investment process will be worked out first with a general risk-averse utility function, and then an optimal strategy with CARA utility will be presented using martingale methods. The optimal investment strategy is analyzed numerically for the CARA utility.