• Selected
• Entire List

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:
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:
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:
This paper considers a max-min formulation of multistage optimal investment and consumption problems, with uncertainties in the form of variable productivities of capital and interest rates. The criterion of control performance is minimum consumption over time, weighted by a coefficient which indicates the likelihood of possible disturbance sequences. A dynamic programming method is used. Explicit results for a max-min formulation of the Merton portfolio optimisation problem are obtained. A production-consumption-debt model arising in international finance is also considered.

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:
We consider an optimal investment model in which the goal is to maximize the long-term growth rate of expected utility of wealth. In the model, the mean returns of the securities are explicitly affected by the underlying economic factors. The utility function is HARA. The problem is reformulated as an infinite time horizon risk-sensitive control problem. We study the dynamic programming equation associated with this control problem and derive some consequences of the investment problem.

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.