Journal of Optimization Theory and Applications

, Volume 166, Issue 3, pp 1029–1050 | Cite as

Optimal Debt Ratio and Consumption Strategies in Financial Crisis

  • Zhuo Jin


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.


Stochastic control Optimal debt ratio Consumption strategies Financial crisis 

Mathematics Subject Classification

91B06 91B40 91B42 91B70 93E20 



The research of Zhuo Jin was supported by the Early Career Research Grant of University of Melbourne and The Fundamental Research Funds for the Central Universities in China.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Centre for Actuarial Studies, Department of EconomicsThe University of MelbourneMelbourneAustralia

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