Application of Stochastic Optimal Control to Financial Market Debt Crises

Jerome Stein

No 2539, CESifo Working Paper Series from CESifo

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.

Keywords: stochastic optimal control; dynamic optimization; mortgage crisis; Ito equation; risk aversion; debt management; warning signals (search for similar items in EconPapers)
JEL-codes: C61 D81 D91 D92 G10 G11 G12 G14 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://www.cesifo.org/DocDL/cesifo1_wp2539.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ces:ceswps:_2539

Access Statistics for this paper

More papers in CESifo Working Paper Series from CESifo Contact information at EDIRC.
Bibliographic data for series maintained by Klaus Wohlrabe ().