Optimal Investment in a Defaultable Bond

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Optimal Investment in a Defaultable Bond

by Peter Lakner of New York University, and
Weijian Liang of New York University

January 12, 2007

Abstract: The present paper analyzes the optimal investment strategy in a defaultable (corporate) bond and a money market account in a continuous time model. 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 small 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.

Keywords: corporate bond, default risk, utility maximization, optimal investment.

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