Optimal Investment under Information Driven Contagious Distress
SIAM Journal on Control and Optimization, Forthcoming
36 Pages Posted: 21 Sep 2015 Last revised: 19 Dec 2016
Date Written: December 18, 2016
We introduce a dynamic optimization framework to analyze optimal portfolio allocations within an information driven contagious distress model. The investor allocates his wealth across several stocks whose growth rates and distress intensities are driven by a hidden Markov chain, and also influenced by the distress state of the economy. We show that the optimal investment strategies depend on the gradient of value functions, recursively linked to each other via the distress states. We establish uniform bounds for the solutions to a sequence of approximation problems, show their convergence to the unique Sobolev solution of the recursive system of Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs), and prove a verification theorem. We provide a numerical study to illustrate the sensitivity of the strategies to contagious distress, stock volatilities and risk aversion.
Keywords: information driven contagion; stochastic control; Nonlinear filtering; Recursive HJB
JEL Classification: G11, G31, C61, C11
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