Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/26584 
Year of Publication: 
2009
Series/Report no.: 
CESifo Working Paper No. 2539
Publisher: 
Center for Economic Studies and ifo Institute (CESifo), Munich
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.
Subjects: 
Stochastic optimal control
dynamic optimization
mortgage crisis
Ito equation
risk aversion
debt management
warning signals
JEL: 
C61
D81
D91
D92
G1
G11
G12
G14
Document Type: 
Working Paper
Appears in Collections:

Files in This Item:
File
Size
374.29 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.