Application of stochastic optimal control to financial market debt crises

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: CESifo Working Paper ; No. 2539

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Criteria for Decision-Making under Risk and Uncertainty ; Micro-Based Behavioral Economics: Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making‡ ; Portfolio Choice; Investment Decisions ; Asset Pricing; Trading Volume; Bond Interest Rates ; Information and Market Efficiency; Event Studies; Insider Trading
• Subject: Stochastic optimal control ; dynamic optimization ; mortgage crisis ; Ito equation ; risk aversion ; debt management ; warning signals ; Schulden ; Kreditrisiko ; Portfolio-Management ; Kontrolltheorie ; Frühwarnsystem ; Hypothek ; Finanzmarktkrise ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Stein, Jerome L.
• Event: Veröffentlichung
• (who): Center for Economic Studies and ifo Institute (CESifo)
• (where): Munich
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/26584
• Last update: 10.03.2025, 11:44 AM CET