Investment and Consumption Problem with Unemployment and Reemployment Driven by Regime Switching

This paper studies an optimal investment and consumption problem for an individual whose employment state is driven by an inhomogeneous Markov chain. We consider two types of individuals distinguished by whether they take the risk of unemployment into consideration when making decisions to maximize the overall consumption and the wealth at retirement. Optimal investment and consumption strategies and the corresponding value function are derived by solving the corresponding regime-switching Hamilton-Jacobi-Bellman equations. By comparing the two types of decision makers, we find it is necessary to consider the unemployment risk. Finally, numerical analysis is provided and it implies that the unemployment will lead to a greater decline in consumption levels for young people than that for elderly people