Portfolio optimization with defaultable securities

In this thesis we derive a closed-form solution for the representative investor who optimally allocates his/her wealth among the following securities: a credit-risky asset (or a defaultable bond), a default-free bank account, and a stock (or index). Although the inclusion of a credit-related financial product in the portfolio selection problem is more realistic, no closed-form solutions to date are given in the literature when a positive recovery value is considered in the event of a default.; The dynamics of a defaultable bond price is derived with the specification of the recovery of market value. We study two different types of utility functions of the representative agent: Constant Relative Risk Aversion utility function and Constant Absolute Risk Aversion utility function. The optimal portfolio problem for the representative investor is solved through the method of stochastic optimal control.; We find that given positive (zero) interest rates the investor will allocate larger (positive) fraction of wealth to the defaultable security as long as the default-event risk is priced. On the other hand, we find that if the default risk premium is not priced, then the investor will invest negative (zero) amount of wealth in the defaultable security. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities.