Optimum consumption and portfolio rules in a continuous-time model

Abstract

This paper presents a stochastic control problem with an inhomogeneous regime switching and applies it to a consumption and investment model. We prove that the inhomogeneous Markov chain is a semimartingale, providing a basis to extend the HJB equations with regime switching to inhomogeneous cases. Explicit solutions are obtained by solving the corresponding HJB equations. Additionally, we study the impact of different levels of unemployment income and intensities of unemployment and reemployment on consumption and value function. Our findings suggest that improving unemployment security and reemployment intensity can increase overall happiness and improve the total value function.