Optimal debt ratio and consumption strategies in financial crisis

This paper derives the optimal debt ratio and consumption strategies for an economy during the financial crisis. Taking into account the impact of labor market condition during the financial crisis, the production rate function is stochastic and affected by the government fiscal policy and unanticipated shocks. The objective is to maximize the total expected discounted utility of consumption in the infinite time horizon. Using dynamic programming principle, the value function is a solution of Hamilton–Jacobi–Bellman (HJB) equation. The subsolution-supersolution method is used to verify the existence of classical solutions of the HJB equation. The explicit solution of the value function is derived, and the corresponding optimal debt ratio and consumption strategies are obtained. An example is provided to illustrate the methodologies and some interesting economic insights.