Application of Stochastic Optimal Control to Financial Market Debt Crises
Jerome L. Stein
Brown University - Division of Applied Mathematics; CESifo (Center for Economic Studies and Ifo Institute)
January 27, 2009
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 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.
Number of Pages in PDF File: 29
Keywords: Stochastic optimal control, Dynamic Optimization, Ito equation, Risk aversion, Debt Management, Mortgage Crisis, Warning signals
JEL Classification: C61, D81, D91, F1, G11, G12, G14
Date posted: January 28, 2009 ; Last revised: January 29, 2009
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