Optimal Portfolio with a Defaultable Bond

In this paper we research a representative investor how to optimally allocate her wealth among the following securities; a defaultable bond, a stock and a bank account.. We model the defaultable bond price through a reduced-form approach and solve the dynamics of its price. Using martingale methods, we obtain a dosed-form solution to this optimal problem. From the solution it is dear that for a jump-risk premium greater than one, namely the market pricing the jump risk in the defaultable bond, the investor will optimally invest a positive amount, in the defaultable bond. On the other hand, the investor will optimally invest nothing in the defaultable bond.