Application of Stochastic Optimal Control to Financial Market Debt Crises
AbstractThis 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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Bibliographic InfoPaper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2539.
Date of creation: 2009
Date of revision:
stochastic optimal control; dynamic optimization; mortgage crisis; Ito equation; risk aversion; debt management; warning signals;
Find related papers by JEL classification:
- 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
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
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- Yuliya Demyanyk & Otto Van Hemert, 2007. "Understanding the subprime mortgage crisis," Supervisory Policy Analysis Working Papers 2007-05, Federal Reserve Bank of St. Louis.
- Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575, September.
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- Kristopher Gerardi & Andreas Lehnert & Shane M. Sherlund & Paul Willen, 2008.
"Making Sense of the Subprime Crisis,"
Brookings Papers on Economic Activity,
Economic Studies Program, The Brookings Institution, vol. 39(2 (Fall)), pages 69-159.
- Kristopher S. Gerardi & Andreas Lehnert & Shane M. Sherlund & Paul S. Willen, 2009. "Making sense of the subprime crisis," Working Paper 2009-02, Federal Reserve Bank of Atlanta.
- 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.
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