Application of Stochastic Optimal Control to Financial Market Debt Crises
29 Pages Posted: 28 Jan 2009 Last revised: 29 Jan 2009
Date Written: January 27, 2009
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 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, Ito equation, Risk aversion, Debt Management, Mortgage Crisis, Warning signals
JEL Classification: C61, D81, D91, F1, G11, G12, G14
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
A Stochastic Optimal Control Approach to International Finance and Foreign Debt
-
Country Default Risk: An Empirical Assessment
By Jerome L. Stein and Giovanna Paladino
-
Efficient Intertemporal Allocations with Recursive Utility
By Bernard Dumas, Tan Wang, ...
-
Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time
By Sid Browne
-
A Tale of Two Debt Crises: A Stochastic Optimal Control Analysis
-
A Tale of Two Debt Crises: A Stochastic Optimal Control Analysis