Abstract
We develop a fixed income portfolio framework which accounts for self-exciting default effects. Our empirically driven credit model captures the contagion mechanism through which the default of an obligor impacts the credit quality of others, as well as the time decaying of contagious effects. We obtain explicit expressions for the optimal feedback strategies as well as for the value function of the dynamic optimization problem. Our formulas indicate that contagion induces the investor to account both for price depreciations and changes in expected investor's utility due to obligors' defaults, when deciding on the optimal strategies. We prove a verification theorem establishing the equivalence between the value function and the solution of a recursive system of HJB-PDEs. Numerical results confirm the high sensitivity of strategies to risk aversion and self-excitation.
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