Optimal Investment under Information Driven Contagious Distress

TL;DR

This paper develops a dynamic optimization model for optimal portfolio allocation considering contagious distress driven by hidden Markov states and economic factors, with solutions linked to complex HJB PDEs.

Contribution

It introduces a novel framework combining contagion, hidden Markov models, and recursive HJB PDEs for optimal investment strategies under economic distress.

Findings

Optimal strategies depend on distress states and their gradients.

Solutions to the recursive PDE system are shown to converge and be unique.

Numerical analysis demonstrates strategy sensitivity to contagion and risk preferences.

Abstract

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.