Stochastic Intertemporal Optimization in Discrete Time (new title: Stochastic optimization in discrete time)

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.

Stochastic Optimal Control, International Finance and Debt

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

Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications

In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation

The Conformation of Interfacially Adsorbed Ranaspumin-2 Is an Arrested State on the Unfolding Pathway

Ranaspumin-2 (Rsn-2) is a surfactant protein found in the foam nests of the t\'{u}ngara frog. Previous experimental work has led to a proposed model of adsorption which involves an unusual clam shell-like `unhinging' of the protein at an interface. Interestingly, there is no concomitant denaturation of the secondary structural elements of Rsn-2 with the large scale transformation of its tertiary structure. In this work we use both experiment and simulation to better understand the driving forces underpinning this unusual process. We develop a modified G\={o}-model approach where we have included explicit representation of the side-chains in order to realistically model the interaction between the secondary structure elements of the protein and the interface. Doing so allows for the study of the underlying energy landscape which governs the mechanism of Rsn-2 interfacial adsorption. Experimentally, we study targeted mutants of Rsn-2, using the Langmuir trough, pendant drop tensiometry and circular dichroism, to demonstrate that the clam-shell model is correct. We find that Rsn-2 adsorption is in fact a two-step process: the hydrophobic N-terminal tail recruits the protein to the interface after which Rsn-2 undergoes an unfolding transition which maintains its secondary structure. Intriguingly, our simulations show that the conformation Rsn-2 adopts at an interface is an arrested state along the denaturation pathway. More generally, our computational model should prove a useful, and computationally efficient, tool in studying the dynamics and energetics of protein-interface interactions.Comment: 8 figure

Distributed Control Design for Balancing the Grid Using Flexible Loads

International audienceInexpensive energy from the wind and the sun comes with unwanted volatility, such as ramps with the setting sun or a gust of wind. Controllable generators manage supply-demand balance of power today, but this is becoming increasingly costly with increasing penetration of renewable energy. It has been argued since the 1980s that consumers should be put in the loop: " demand response " will help to create needed supply-demand balance. However, consumers use power for a reason, and expect that the quality of service (QoS) they receive will lie within reasonable bounds. Moreover, the behavior of some consumers is unpredictable, while the grid operator requires predictable controllable resources to maintain reliability. The goal of this chapter is to describe an emerging science for demand dispatch that will create virtual energy storage from flexible loads. By design, the grid-level services from flexible loads will be as controllable and predictable as a generator or fleet of batteries. Strict bounds on QoS will be maintained in all cases. The potential economic impact of these new resources is enormous. California plans to spend billions of dollars on batteries that will provide only a small fraction of the balancing services that can be obtained using demand dispatch. The potential impact on society is enormous: a sustainable energy future is possible with the right mix of infrastructure and control systems