We consider the problem of maximizing expected utility from terminal wealth for a power investor who can allocate his wealth in a stock, a defaultable bond, and a   money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain . By means of a reference probability approach to filtering in the enlarged market filtration , we reduce the partially observed stochastic control problem to a  risk sensitive control problem with full observation . We separate the latter into a pre-default and a post-default dynamic optimization subproblems, and obtain two coupled Hamilton-Jacobi-Bellman equations for the optimal value functions. We obtain a complete solution to the post-default optimization subproblem, and prove a verification theorem for the solution of the pre-default optimization subproblem .
We consider the problem of maximizing expected utility from terminal wealth for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain . We reduce the partially observed stochastic control problem to a complete observation risk sensitive control problem via the filtered regime switching probabilities . We separate the latter into a pre-default and a post-default dynamic optimization subproblems, and obtain two coupled Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical solution to the pre-default HJB equation, and give a verification theorem characterizing each value function as the solution of the corresponding HJB equation. We provide a detailed numerical analysis showing that the investor increases his stock holdings as the filter probability of being in the high growth regime increases, and decreases his credit risk exposure when the filter probability of being in the high default risk regime gets larger. We find that the investor increases the fraction of overall wealth invested in the risky asset when the information gain coming from receiving price observations is higher .
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a
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defaultable bond, and
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defaultable security, and
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a
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. By means of a reference probability approach to filtering in the enlarged market filtration
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, we
. We
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complete observation
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with full observation
via the filtered regime switching probabilities
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equations for the optimal value functions. We obtain a complete
(HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical
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post-default optimization subproblem, and prove
pre-default HJB equation, and give
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for
characterizing each value function as
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pre-default optimization subproblem
corresponding HJB equation. We provide a detailed numerical analysis showing that the investor increases his stock holdings as the filter probability of being in the high growth regime increases, and decreases his credit risk exposure when the filter probability of being in the high default risk regime gets larger. We find that the investor increases the fraction of overall wealth invested in the risky asset when the information gain coming from receiving price observations is higher