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We consider a portfolio optimization problem in a defaultable market withfinitely-many economical regimes, where the investor can dynamically allocateher wealth among a defaultable bond, a stock, and a money market account. Themarket coefficients are assumed to depend on the market regime in place, whichis modeled by a finite state continuous time Markov process. We rigorouslydeduce the dynamics of the defaultable bond price process in terms of a Markovmodulated stochastic differential equation. Then, by separating the utilitymaximization problem into the pre-default and post-default scenarios, we deducetwo coupled Hamilton-Jacobi-Bellman equations for the post and pre-defaultoptimal value functions and show a novel verification theorem for theirsolutions. We obtain explicit optimal investment strategies and value functionsfor an investor with logarithmic utility. We finish with an economic analysisin the case of a market with two regimes and homogenous transition rates, andshow the impact of the default intensities and loss rates on the optimalstrategies and value functions.

Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching