برنامه های کاربردی از کنترل بهینه تصادفی / برنامه نویسی پویا برای امور مالی بین المللی و بحران بدهی

In July 1997, the economies of East Asia became embroiled in one of the worst financial crises of the postwar period. In 2001 Argentina defaulted on its sovereign debt. Prior to the crises, the markets and the International Monetary Fund viewed these economies as models of growth and stability. We use stochastic optimal control and dynamic programming to model an optimal foreign debt and show why divergences of the actual debt from the optimal make the economies vulnerable to crises. These divergences imply measurable warning signals. We provide examples of the derived warning signals for Korea and Argentina.

A major part of the mathematical finance literature has been concerned with intertemporal optimization and risk management of portfolios. The seminal work was by Robert Merton, Continuous Time Finance (1990). Wendell Fleming, his co-authors and others influenced by his work, have made the subsequent major contributions. The articles use the techniques of stochastic optimal control/dynamic programming (SOC/DP), and successively consider ever more interesting, difficult and realistic modeling of both the uncertainty and the constraints. Comprehensive evaluations of this mathematical literature are by Fleming [1], [2] and [3]. Recently, Fleming and Stein [5] and [6], Stein [7], Stein and Lim [8], Stein and Paladino [9] have applied the techniques of SOC/DP to the modeling of debt crises. The aim of this interdisciplinary paper is to explain the logic of the modeling and the ability of this approach to derive warning signals of debt crises. 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. Similarly in 1998, the financial markets and the International Monetary Fund viewed Argentina as a model of stability and growth. However in 2001–02 the Argentine economy defaulted on its huge debt. Why did the market not anticipate the crises? To this end, we use SOC/DP to model an optimal foreign debt, and show 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. We provide examples of these warning signals for Korea and Argentina.