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A Stochastic Optimal Control Approach to International Finance and Foreign Debt

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  • Wendell Fleming
  • Jerome L. Stein

Abstract

The recent financial crises, especially the debt crisis in Asia, have led to questions su ch as: what are their causes, what is an excessive debt and how vulnerable is an economy to external shocks? We develop an economic model of international finance and debt based upon two sources of uncertainty: the productivity of capital and the real int e rest rate. We use stochastic optimal control-dynamic programming to derive the: optimal consumption, foreign debt, capital, the growth of net worth and the current account. The objective is to maximize the expectation of the discounted value of the utilit y of consumption over an infinite horizon. Crises - and associated social unrest - occur when the unanticipated shocks produce a significant decline in the utility of consumption. We relate our optimality conditions to the vulnerability of the economy to crises. The major conclusions are as follows. (1) We derive explicit and implementable closed form equations for the optimum debt/net worth, which maximize the expectation of the discounted value of utility over an infinite horizon. (2) The derived debt/net worth ratio also maximizes the expected growth of net worth, given any fixed consumption/net worth ratio. (3) The vulnerability of an economy to shocks is positively related to the variance of the utility of consumption at any time. We derive a risk-exp ected return tradeoff. When the debt exceeds the optimum, there is inefficiency. The expected growth of the utility of consumption can be increased, and the vulnerability of the economy - measured by the variance of the utility of consumption - can be decreased by decreasing the debt/net worth ratio.

Suggested Citation

  • Wendell Fleming & Jerome L. Stein, 1999. "A Stochastic Optimal Control Approach to International Finance and Foreign Debt," CESifo Working Paper Series 204, CESifo.
    • Handle: RePEc:ces:ceswps:_204
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    References listed on IDEAS

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    1. Graciela Kaminsky & Saul Lizondo & Carmen M. Reinhart, 1998. "Leading Indicators of Currency Crises," IMF Staff Papers, Palgrave Macmillan, vol. 45(1), pages 1-48, March.
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    3. Graciela Laura Kaminsky, 1997. "Leading Indicators of Currency Crises," IMF Working Papers 1997/079, International Monetary Fund.
    4. Carmen M. Reinhart & Graciela L. Kaminsky, 1999. "The Twin Crises: The Causes of Banking and Balance-of-Payments Problems," American Economic Review, American Economic Association, vol. 89(3), pages 473-500, June.
    5. Milesi-Ferretti, G-M & Razin, A, 1996. "Current-Account Sustainability," Princeton Studies in International Economics 81, International Economics Section, Departement of Economics Princeton University,.
    6. Kaminsky, Graciela L. & Reinhart, Carmen M., 2000. "On crises, contagion, and confusion," Journal of International Economics, Elsevier, vol. 51(1), pages 145-168, June.
    7. Ettore F. Infante & Jerome L. Stein, 1973. "Optimal Growth with Robust Feedback Control," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(1), pages 47-60.
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    Cited by:

    1. Jerome L. Stein & Giovanna Paladino, 2001. "Country Default Risk: An Empirical Assessment," Australian Economic Papers, Wiley Blackwell, vol. 40(4), pages 417-436, December.
    2. Tina Engler & Alfons Balmann, 2015. "On Investment Consumption Modeling with Jump Process Extensions for Productive Sectors," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 949-958, December.
    3. Chen, Xu & Yang, Xiang-qun, 2015. "Optimal consumption and investment problem with random horizon in a BMAP model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 197-205.
    4. Wendell Fleming, 2000. "Stochastic Intertemporal Optimization in Discrete Time (new title: Stochastic optimization in discrete time)," CESifo Working Paper Series 338, CESifo.

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