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US Financial Debt Crisis: A Stochastic Optimal Control Approach

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  • Stein Jerome L.

    (Professor of Economics (Emeritus), Research Professor Division Applied Mathematics, Brown University, Box F, Providence Rl 02912 USA)

Abstract

The financial crisis was precipitated by the mortgage crisis. A whole structure of financial derivatives was based upon the ultimate debtors, the mortgagors. Insofar as the mortgagors were unable to service their debts, the values of the derivatives fell. The financial intermediaries whose assets and liabilities were based upon the value of derivatives were very highly leveraged. Changes in the values of their net worth were large multiples of changes in asset values. A cascade was precipitated by the mortgage defaults. In this manner, the mortgage debt crisis turned into a financial crisis. The crucial variable is the optimal debt of the real estate sector, which depends upon the capital gain and the interest rate. I apply the Stochastic Optimal Control (SOC) analysis to derive the optimal debt. Two models of the stochastic process on the capital gain and interest rate are presented. Each implies a different value of the optimal debt/net worth. I derive an upper bound of the optimal debt ratio, based upon the alternative models. An empirical measure of the excess debt: actual less the upper bound of the optimal ratio, is shown to be an early warning signal (EWS) of the debt crisis.

Suggested Citation

  • Stein Jerome L., 2011. "US Financial Debt Crisis: A Stochastic Optimal Control Approach," Review of Economics, De Gruyter, vol. 62(3), pages 197-217, December.
    • Handle: RePEc:lus:reveco:v:62:y:2011:i:3:p:197-217
    DOI: 10.1515/roe-2011-0301
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    References listed on IDEAS

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    1. Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575, Decembrie.
    2. Fleming, Wendell H. & Stein, Jerome L., 2004. "Stochastic optimal control, international finance and debt," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 979-996, May.
    3. Stein, Jerome L., 2011. "The crisis, Fed, Quants and stochastic optimal control," Economic Modelling, Elsevier, vol. 28(1-2), pages 272-280, January.
    4. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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