Optimal Investment Under Information Driven Default Contagion

Abstract

We introduce a novel dynamic optimization framework to analyze optimal portfolio allocations within an information driven default contagion model. The investor allocates his wealth across several defaultable stocks whose growth rates and default intensities are driven by a hidden Markov chain. We provide a rigorous analysis of default contagion arising through recursive dependence of the optimal strategies on the gradient of value functions. We establish uniform bounds for solutions to a sequence of approximation problems, show their convergence to the unique Sobolev solution of a recursive system of Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs), and prove the corresponding verification theorem. We provide a numerical study to illustrate the sensitivity of the strategies to default contagion, stock volatility, and risk aversion.