Dynamic Credit Investment in Partially Observed Markets

TL;DR

This paper develops a framework for optimizing investment strategies in markets with hidden regimes, using stochastic control and filtering techniques to adapt to changing economic conditions.

Contribution

It introduces a method to solve partially observed stochastic control problems by reducing them to risk-sensitive control problems with coupled HJB equations, including existence and uniqueness results.

Findings

Investor increases stock holdings in high growth regimes.

Investor reduces credit risk exposure in high default risk regimes.

Numerical analysis confirms adaptive investment behavior.

Abstract

We consider the problem of maximizing expected utility 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 pre-default and 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 each HJB equation, and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high growth regimes increases, and decreases his credit risk exposure when the filter probability of being in high default risk regimes gets larger.