A finite-horizon optimal investment and consumption problem using regime-switching models (Q2874733)

The paper considers a simple but interesting variant of the classical problem of maximizing utility from consumption, when asset prices follow constant coefficient diffusion processes. Here the drift and diffusion coefficients, as well as the riskless rate, depend on a finite state Markov chain assumed to be independent of the underlying Brownian motions. Interestingly, the instantaneous utility function is itself depending on the prevailing state of the Markov process. Maximizing discounted, expected utility from intermediate consumption and terminal wealth under a non negativity constraint on wealth is obtained via Hamilton-Jacobi-Bellman, as shown in Theorem 3.1. An explicit solution is given for the case of a power utility function.