Optimal investment in a defaultable bond

The present paper analyzes the optimal investment strategy in a defaultable (corporate) bond and a money market account in a continuous time model. Due to jumps in the bond price our market model is incomplete. The treatment of information on the firm's asset value is based on an approach unifying the structural model and the reduced-form model. Specifically, the asset value will be assumed to be observable only at finitely many time points before the maturity of the bond. The optimal investment process will be worked out first for a short time-horizon with a general risk-averse utility function, then a multi-period optimal strategy with logarithmic and power utility will be presented using backward induction. The optimal investment strategy is analyzed numerically for the logarithmic utility.