• Selected
• Entire List

Abstract:
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

Abstract:
The recent financial crises, especially the debt crisis in Asia, have led to questions such as: what are their causes, what is an excessive debt and how vulnerable is an economy to external shocks; We develop an economic model of international finance and debt based upon two sources of uncertainty: the productivity of capital and the real interest rate. We use stochastic optimal control-dynamic programming to derive the: optimal consumption, foreign debt, capital, the growth of net worth and the current account. The objective is to maximize the expectation of the discounted value of the utility of consumption over an infinite horizon. Crises ; and associated social unrest ; occur when the unanticipated shocks produce a significant decline in the utility of consumption. We relate our optimality conditions to the vulnerability of the economy to crises. The major conclusions are as follows. (1) We derive explicit and implementable closed form equations for the optimum debt/net worth, which maximize the expectation of the discounted value of utility over an infinite horizon. (2) The derived debt/net worth ratio also maximizes the expected growth of net worth, given any fixed consumption/net worth ratio. (3) The vulnerability of an economy to shocks is positively related to the variance of the utility of consumption at any time. We derive a risk-expected return tradeoff. When the debt exceeds the optimum, there is inefficiency. The expected growth of the utility of consumption can be increased, and the vulnerability of the economy ; measured by the variance of the utility of consumption ; can be decreased by decreasing the debt/net worth ratio.

Stochastic optimal control, foreign debt, international finance, current account, vulnerability to external shocks

Abstract:
Banks should evaluate whether a borrower is likely to default. I apply several techniques in the extensive mathematical literature of stochastic optimal control/dynamic programming to derive an optimal debt in an environment where there are risks on both the asset and liabilities sides. The vulnerability of the borrowing firm to shocks from either the return to capital, the interest rate or capital gain, increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. As the debt ratio exceeds the optimum, default becomes ever more likely. This paper is "A Tale of Two Crises" because the analysis is applied to the agricultural debt crisis of the 1980s and to the sub-prime mortgage crisis of 2007. A measure of excess debt is derived, and we show that it is an early warning signal of a crisis.

optimization, banking, stochastic optimal control, agriculture debt crisis, subprime mortgage crisis

Abstract:
The ultimate object of research concerning the Euro is to answer the following questions: (#1) What is the equilibrium trajectory of the nominal euro, measured as dollars/euro? (#2) To what extent has the equilibrium nominal euro been determined by relative prices (PPP), and to what extent has it been determined by real fundamentals? (#3) How important have been the transitory factors in affecting the value of the euro? (#4) Is the euro currently undervalued, and by what criteria? Our evaluation of recent research concerning the answers to these questions, is the subject of this paper.

Euro, NATREX, BEER, Equilibrium Exchange Rates, International Capital Flows, Misalignment

Abstract:
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

Abstract:
We use stochastic optimal control-dynamic programming (DP) to derive the optimal foreign debt/net worth, consumption/net worth, current account/net worth, and endogenous growth rate in an open economy. Unlike the literature that uses an Intertemporal Budget Constraint (IBC) or the Maximum Principle, the DP approach does not require perfect foresight or certainty equivalence. Errors of measurement and the effects of unanticipated shocks are corrected in an optimal manner. We contrast the DP and IBC approaches, show how the results of the dynamic programming approach can be interpreted in a traditional simple mean-variance/Tobin-Markowitz context, and explain why our results are generalizations of the Merton model.

Stochastic Optimal Control, Foreign Debt, International Finance, Vulnerability to External Shocks, Sustainable Current Account Deficits

Abstract:
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

Abstract:
This paper provides a consistent theoretical framework to explain the fundamental determinants of the evolution in the medium to longer run of the real effective exchange rate of the United States relative to the currencies of the other G-7 countries. The fundamental determinants are productivity and thrift in the United States and the other major industrial countries. The real rate generated by these fundamentals is referred to as the natural real exchange rate (NATREX). Then, using cointegrating and error correction analysis, the paper examines the explanatory power of the NATREX model to explain the evolution of the real exchange rate of the U.S. dollar during the floating exchange rate period.

Abstract:
The standard literature concerning intertemporal optimization in international finance is based upon certainty equivalence, and ignores risk and uncertainty. It therefore is not helpful concerning risk management and evaluation of the risk involved in the holding of international short-term debt. We solve a modification of the standard model of intertemporal optimization in discrete time, in an environment where the return to capital is stochastic. We impose the constraint that there be no default on the short-term debt. Thereby we derive benchmarks for optimal foreign debt, which will not be defaulted. We do not claim that the optimal debt is the same as the actual debt incurred. Witness the defaults and debt crises. Insofar as the actual debt exceeds the benchmark, the risk of default is increased. The main reasons for a deviation between the actual debt and the optimal debt is that the borrower is overly optimistic about the distribution function of the return to investment, and does not optimize subject to a "no default" constraint. We also consider an intertemporal optimization model involving extreme prudence. The lender, who may be an institutional investor, has infinite risk aversion and will only lend for projects where the profitability of the investment is almost sure. In this case also, we derive the optimal debt, which is our benchmark for risk management.

Abstract:
The problem is to evaluate the likelihood that a country will face a currency or balance of payments crisis over a given horizon. When is it rational for market participants to expect a depreciation of the currency? On the basis of considerable empirical studies we know that in both banking and currency crises, there is a multitude of weak and deteriorating economic fundamentals. Our theme is that there is an economic logic to medium and longer-term movements in exchange rates, within the context of a consistent dynamic stock-flow model. The equilibrium real exchange rate is a trajectory, not a point. We provide objective measures of the real fundamentals that determine the moving equilibrium real exchange rate, and explain the dynamic economic mechanism whereby the actual exchange rate converges to this moving equilibrium exchange rate, called the NATREX. The fundamentals are primarily social consumption/GDP, which is generally driven by fiscal policy, and the productivity of the economy. Trends in social consumption/GDP, and in fiscal policy, reflected political regime changes in France, Germany and Italy.

Abstract:
The focus is upon equilibrium real exchange rates, optimal external debt and their interaction, in a world where both the return on investment and the real rate of interest are stochastic variables. These theoretically based measures are applied empirically to answer the following questions: What is a theoretically based empirical measure of an excess debt that increases the probability of a debt crisis? What is a theoretically based empirical measure of a misaligned exchange rate that increases the probability of a currency/balance of payments crises? Two theoretical tools are used to derive Early Warning Signals. One is the NATREX model to estimate the equilibrium real exchange rate. The second is stochastic optimal control/dynamic programming to derive the optimal debt and endogenous growth rate. Examples are given of these applications.

stochastic optimal control, foreign debt, NATREX, vulnerability to external shocks, sustainable current account, warning signals of debt crisis, exchange rate misalignments

Abstract:
This paper applies the NATREX model of equilibrium exchange rates to evaluate several key studies of the Central and Eastern European Countries (CEEC) in general, with particular emphasis upon the Czech Republic and Hungary and with references to Poland and Bulgaria. On the basis of the NATREX model, we evaluate several key studies to answer the questions: How can the trends in the real exchange rates of the transition economies be explained? What are sustainable trends in their real exchange rates? To what extent were the real exchange rates misaligned? What are sustainable/equilibrium current account deficits and net investment positions in the medium and in the long-run? What are the policy implications for the transition economies of the NATREX analysis?

transition economies, NATREX model, equilibrium real exchange rates, current account deficits, euro area

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.

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

Abstract:
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

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.

Stochastic optimal control, Dynamic Optimization, Ito equation, Risk aversion, Debt Management, Mortgage Crisis, Warning signals

Abstract:
The International Monetary Fund, the World Bank and the bond rating agencies did not anticipate the crises in Asia 1997-98 and in Argentina 2001. With this statement in mind, we consider some multi-stage inter-temporal stochastic optimisation models in international finance that imply theoretically founded and empirically measurable Early Warning Signals. The mathematical technique is dynamic programming/stochastic optimal control (DP/SOC).

The variables of interest are the optimal foreign debt, consumption, capital and the growth rate of GDP. They are used as benchmarks of economic performance. By comparing the actual debt to the optimal debt we derive a measure of the sustainability of the debt and vulnerability to default problems. The two sources of uncertainty - the productivity of capital and the real interest rate on the foreign debt - are modeled as stochastic processes. Specific applications of the DP/SOC techniques are given for country defaults in Asia and Latin America, and the US current account deficits.

Abstract:
The EMU is in the process of expanding its membership. How will the expansion affect the equilibrium or sustainable real value of the euro? What is the explanatory power of the model used to explain the equilibrium value of a synthetic euro? We then demonstrate quantitatively the dynamic effects of enlargement upon the equilibrium value of the euro under different scenarios.

Abstract:
The papers in this issue are concerned with the behaviour of exchange rates - their fundamental determinants, adjustment processes and policy implications. The authors combine theory with empirical evidence, test hypotheses as well as show the relevance of their analysis for policy. This Introduction addresses several questions. What are the contributions of the articles to the economics of exchange rates? Are they significant in increasing our understanding of the current issues and in addressing questions of policy? How can one explain the movements in the European and the Asian currencies? What can we expect to happen to the euro with the enlargement of the euro area? Do the papers provide frameworks to guide empirical research? In this Introduction, we highlight aspects of each paper that addresses these issues.

Abstract:
The standard model of inter-temporal optimization is based upon certainty equivalence and ignores risk and uncertainty. We solve a modification of the standard model of inter-temporal optimization in an environment where the return to capital is stochastic, and we impose the constraint that there be no default on the short-term debt. We derive benchmarks for optimal foreign debt in a world of uncertainty. Insofar as the actual debt exceeds the benchmark, the expected utility of consumption is reduced. Default occurs with probability (1-p) when the debt exceeds the maximum debt f(2)max. The main reasons for a deviation between the actual debt and the optimal debt are that the borrower is overly optimistic about the distribution function of the return to investment, does not optimize with the "no default" constraint, and/or there is a moral hazard problem. We also consider an inter-temporal optimization model involving extreme prudence. The lender, who may be an institutional investor, has infinite risk aversion and will only lend for projects where the profitability of the investment is almost sure. In this case also, we derive the optimal debt, which is our benchmark for risk management.

Stochastic inter-temporal optimization, international debt, uncertainty, risk

Abstract:
Data on the credit rating of bonds issued in the first half of the 1990s suggest that investors in emerging market securities paid little attention to credit risk, or that they were comfortable with the high level of credit risk that they were incurring. The literature in international finance concerning inter-temporal optimization in discrete time makes assumptions that imply certainty equivalence. Example: If the expected productivity of capital is a constant that exceeds the interest rate, investment and debt are maximal. There is a need for a "paradigm shift" that involves greater analytic emphasis on the risks associated with the reliance on short-term debt for otherwise creditworthy borrowers.

Using stochastic optimal control techniques, we develop a paradigm for risk management, with the constraint that there be no default on short-term foreign currency denominated debt. We solve for the constrained optimal investment and external debt in both a finite horizon discrete time and an infinite horizon continuous time context. We thereby derive benchmarks to compare the actual with the constrained optimal debt. The probability of default/rescheduling increases when our constrained optimality conditions are violated.

The main reason for a deviation between the actual debt and the optimal debt is the moral hazard that has been stressed in the literature on crises. The government provides implicit insurance that induces firms to ignore/underemphasize risk. Bubbles tend to occur. However, when the shocks occur, the government cannot fulfill its commitments.

Abstract:
Data on the credit rating of bonds issued in the first half of the 1990s suggest that investors in emerging market securities paid little attention to credit risk, or that they were comfortable with the high level of credit risk that they were incurring. The literature in international finance concerning inter-temporal optimization in discrete time makes assumptions that imply certainty equivalence. Example: If the expected productivity of capital is a constant that exceeds the interest rate, investment and debt are maximal. There is a need for a "paradigm shift" that involves greater analytic emphasis on the risks associated with the reliance on short-term debt for otherwise creditworthy borrowers.

Using stochastic optimal control techniques, we develop a paradigm for risk management, with the constraint that there be no default on short- term foreign currency denominated debt. We solve for the constrained optimal investment and external debt in both a finite horizon discrete time and an infinite horizon continuous time context. We thereby derive benchmarks to compare the actual with the constrained optimal debt. The probability of default/rescheduling increases when our constrained optimality conditions are violated.

The main reason for a deviation between the actual debt and the optimal debt is the moral hazard that has been stressed in the literature on crises. The government provides implicit insurance that induces firms to ignore/underemphasize risk. Bubbles tend to occur. However, when the shocks occur, the government cannot fulfill its commitments.

Abstract:
First: we explain, within the context of a theoretically consistent model, what are the fundamental external and internal determinants of the real effective exchange rate of Germany. Second: we explain how one should view the real effective exchange rate in evaluating the competitiveness of the German economy.