Application of Stochastic Optimal Control to Financial Market Debt Crises

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.stochastic optimal control, dynamic optimization, mortgage crisis, Ito equation, risk aversion, debt management, warning signals

Stochastic Optimal Control Modeling of Debt Crises

What is an optimal or a sustainable external debt - for a country, region or sector? How should one monitor and evaluate debt to preclude a crisis? We use stochastic optimal control/dynamic programming to derive an optimal debt. The deviation of the actual from the optimal will serve as a Warning Signal of a crisis. There is a correspondence between Hamilton-Jacobi-Bellman equation of Dynamic Programming and the static Mean-Variance (M-V) analysis in finance. A graphic analysis of M-V is helpful to explain the implications of DP. An explicit example is the US Agricultural debt crisis.stochastic optimal control, debt, international finance, US agricultural crisis, Mean-Variance analysis, Hamilton-Jacobi-Bellaman equation

Greenspan, Dodd-Frank and Stochastic Optimal Control

Finanzmarkt; Regulierung; Zentralbank; Kontrolltheorie; USA

Country Default Risk: An Empirical Assessment

We provide benchmarks to evaluate what is an optimal foreign debt and a maximal foreign debt (debt-max), when risk is explicitly considered. When the actual debt exceeds debt-max, then the economy will default when a "bad shock" occurs. This paper is an application of the stochastic optimal controls models of Fleming and Stein (2001), which gives empirical content to the question of how one should measure "vulnerability" to shocks, when there is uncertainty concerning the productivity of capital. We consider two sets of high- risk countries during the period 1978-99: a subset of 21 countries that defaulted on the debt, and another set of 13 countries that did not default. Default is a situation where the firms or government of a country reschedule the interest/principal payments on the external debt. We thereby explain how our analysis can anticipate default risk, and add another dimension to the literature of early warning signals of default/credit risk.Default risk, foreign debt, stochastic optimal control, debt rescheduling, uncertainty

Asian Crises: Theory, Evidence, Warning-Signals

In July 1997, the economies of East Asia became embroiled in one of the worst financial crises of the postwar period. Yet, prior to the crisis, these economies were seen as models of economic growth experiencing sustained growth rates that exceeded those earlier thought unattainable. Why did the market not anticipate the crises? To this end, we review the Asian financial crisis from two related perspectives - whether the crisis was precipitated by a failure of the real exchange rate to be aligned with its fundamental determinants and/or whether the crisis was precipitated by a divergence of the foreign debt from its optimal path. The first perspective is based on a coherent theory of the equilibrium real exchange rate - the NATREX model - that shows how “misalignments” lead to currency crises. The second perspective is based on a model of optimal foreign debt ratio - derived from stochastic optimal control - which shows why “divergences” lead to debt crises. The important point here is that these models suggest important variables which may serve as warning signals to predict crises.Asian crises, optimal debt, equilibrium exchange rates, NATREX, stochastic optimal control, warning signals of crises, exchange rate misalignment

United States Current Account Deficits: A Stochastic Optimal Control Analysis

The "Pessimists" and the "Optimists" disagree whether the US external deficits and the associated buildup of US net foreign liabilities are problems that require urgent attention. A warning signal should be that the debt ratio deviates significantly from the optimal ratio. The optimal debt ratio or debt burden should take into account the vulnerability of consumption to shocks from the productivity of capital, the interest rate and exchange rate. The optimal debt ratio is derived from inter-temporal optimization using Dynamic Programming, because the shocks are unpredictable, and it is essential to have a feedback control mechanism. The optimal ratio depends upon the risk adjusted net return and risk aversion both at home and abroad. On the basis of alternative estimates, we conclude that the Pessimists' fears are justified on the basis of trends. The trend of the actual debt ratio is higher than that of the optimal ratio. The Optimists are correct that the current debt ratio is not a menace, because the current level of the debt ratio is not above the corresponding level of the optimum ratio.U.S. current account deficits, external debt, stochastic optimal control, dynamic programming, inter-temporal optimization