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Application of Stochastic Optimal Control to Financial Market Debt Crises

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  • Jerome L. Stein

Abstract

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis.

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File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2009/wp-cesifo-2009-02/cesifo1_wp2539.pdf
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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2539.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2539

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Related research

Keywords: stochastic optimal control; dynamic optimization; mortgage crisis; Ito equation; risk aversion; debt management; warning signals;

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  1. Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575.
  2. Kristopher S. Gerardi & Andreas Lehnert & Shane M. Sherlund & Paul S. Willen, 2009. "Making sense of the subprime crisis," Public Policy Discussion Paper 09-1, Federal Reserve Bank of Boston.
  3. 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.
  4. 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.
  5. Yuliya Demyanyk & Otto Van Hemert, 2007. "Understanding the subprime mortgage crisis," Supervisory Policy Analysis Working Papers 2007-05, Federal Reserve Bank of St. Louis.
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