A Tale of Two Debt Crises: A Stochastic Optimal Control Analysis
AbstractBanks should evaluate whether a borrower is likely to default. I apply several techniques in the extensive mathematical literature of stochastic optimal control/dynamic programming to derive an optimal debt in an environment where there are risks on both the asset and liabilities sides. The vulnerability of the borrowing firm to shocks from either the return to capital, the interest rate or capital gain, increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. As the debt ratio exceeds the optimum, default becomes ever more likely. This paper is “A Tale of Two Crises” because the analysis is applied to the agricultural debt crisis of the 1980s and to the sub-prime mortgage crisis of 2007. A measure of excess debt is derived, and we show that it is an early warning signal of a crisis.
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Bibliographic InfoPaper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2220.
Date of creation: 2008
Date of revision:
optimization; banking; stochastic optimal control; agriculture debt crisis; subprime mortgage crisis;
Other versions of this item:
- Stein, Jerome L., 2010. "A tale of two debt crises: a stochastic optimal control analysis," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 4(3), pages 1-24.
- Stein, Jerome L., 2009. "A tale of two debt crises: a stochastic optimal control analysis," Economics Discussion Papers 2009-44, Kiel Institute for the World Economy.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
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- Massimo Guidolin & Elizabeth A. La Jeunesse, 2007. "The decline in the U.S. personal saving rate: is it real and is it a puzzle?," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 491-514.
- Jerome L. Stein, 2006.
"United States Current Account Deficits: A Stochastic Optimal Control Analysis,"
CESifo Working Paper Series
1805, CESifo Group Munich.
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- Jerome L. Stein, 2005. "Optimal Debt And Endogenous Growth In Models Of International Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 389-413, December.
- Fleming, Wendell H. & Stein, Jerome L., 2004.
"Stochastic optimal control, international finance and debt,"
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Elsevier, vol. 28(5), pages 979-996, May.
- Wendell Fleming & Jerome L. Stein, 2002. "Stochastic Optimal Control, International Finance and Debt," CESifo Working Paper Series 744, CESifo Group Munich.
- Blanchet-Scalliet, Christophette & Diop, Awa & Gibson, Rajna & Talay, Denis & Tanre, Etienne, 2007. "Technical analysis compared to mathematical models based methods under parameters mis-specification," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1351-1373, May.
- Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575, Octomber.
- Stein, Jerome L., 2011.
"The crisis, Fed, Quants and stochastic optimal control,"
Elsevier, vol. 28(1), pages 272-280.
- Stein, Jerome L., 2011. "The crisis, Fed, Quants and stochastic optimal control," Economic Modelling, Elsevier, vol. 28(1-2), pages 272-280, January.
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