Explore the vast range of titles available.

The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives.

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.

We combine ideas from machine learning (ML) and operations research and management science (OR/MS) in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a departure from other work on data-driven optimization, we consider data consisting, not only of observations of quantities with direct effect on costs/revenues, such as demand or returns, but also predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate how our proposed methods are generally applicable to a wide range of decision problems and prove that they are computationally tractable and asymptotically optimal under mild conditions, even when data are not independent and identically distributed and for censored observations. We extend these to the case in which some decision variables, such as price, may affect uncertainty and their causal effects are unknown. We develop the coefficient of prescriptiveness P to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. We demonstrate our approach in an inventory management problem faced by the distribution arm of a large media company, shipping 1 billion units yearly. We leverage both internal data and public data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, account for an 88% improvement as measured by our coefficient of prescriptiveness. This paper was accepted by Noah Gans, optimization.

Uncertainty about future economic and climate conditions substantially affects the choice of policies for managing interactions between the climate and the economy. We develop a framework of dynamic stochastic integration of climate and economy, and show that the social cost of carbon is substantially affected by both economic and climate risks and is a stochastic process with significant variation. We examine a wide but plausible range of values for critical parameters with robust results and show that large-scale computing makes it possible to analyze policies in models substantially more complex and realistic than usually used in the literature.

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols. Here, we obtain the general solution for the distribution of processes in which waiting times between reset events are drawn from an arbitrary distribution. This allows for the investigation of a broader class of much more realistic processes. As an example, our results are applied to the analysis of the efficiency of constrained random search processes.

Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. We investigate a complementary, stochastic approach to reducing errors: Instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. A 70% reduction in the quasiparticle density results in a threefold enhancement in qubit relaxation times and a comparable reduction in coherence variability.

Are business cycles mainly a response to persistent exogenous shocks, or do they instead reflect a strong endogenous mechanism which produces recurrent boom-bust phenomena? In this paper we present evidence in favor of the second interpretation and we highlight the set of key elements that influence our answer. The elements that tend to favor this type of interpretation of business cycles are (i) slightly extending the frequency window one associates with business cycle phenomena, (ii) allowing for strategic complementarities across agents that arise due to financial frictions, and (iii) allowing for a locally unstable steady state in estimation.

We introduce a simple model of dynamic matching in networked markets, where agents arrive and depart stochastically and the composition of the trade network depends endogenously on the matching algorithm. If the planner can identify agents who are about to depart, then waiting to thicken the market substantially reduces the fraction of unmatched agents. If not, thenmatching agents greedily is close to optimal. We specify conditions under which local algorithms that choose the right time to match agents, but do not exploit the global network structure, are close to optimal. Finally, we consider a setting where agents have private information about their departure times and design a mechanism to elicit this information.

We propose a new model for measuring uncertainty and its effects on the economy, based on a large vector autoregression with stochastic volatility driven by common factors representing macroeconomic and financial uncertainty. The uncertainty measures reflect changes in both the conditional mean and volatility of the variables, and their impact on the economy can be assessed within the same framework. Estimates with U.S. data show substantial commonality in uncertainty, with sizable effects of uncertainty on key macroeconomic and financial variables. However, historical decompositions show a limited role of uncertainty shocks in macroeconomic fluctuations.