This second BiBoS volume surveys recent developments in the theory of stochastic processes. Particular attention is given to the interaction between mathematics and physics. Main topics include: statistical mechanics, stochastic mechanics, differential geometry, stochastic proesses, quantummechanics, quantum field theory, probability measures, central limit theorems, stochastic differential equations, Dirichlet forms.

This is an excerpt from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. This extract concentrates on finance.

In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

General Equilibrium, Growth, and Trade: Essays in Honor of Lionel McKenzie provides information pertinent to the three main areas of Professor McKenzie's scientific research, namely, international trade, economic growth, and general equilibrium theory. This book highlights the main aspects of McKenzie's work. Organized into three parts encompassing 21 chapters, this book begins with an overview of the regularizing effects of aggregation over nonregular microrelations. This text then examines the theory of a multiperiod monopolist incurring nonseparable labor adjustment costs, which is developed when investment is irreversible. Other chapters consider the behavior of a price-maker in a competitive market as a preliminary step to a more complete analysis of pure competition. This book discusses as well the effects of uncertainty on optimal decisions, which constitutes an increasingly essential area of economic research. The final chapter deals with the general equilibrium macroeconomic model. This book is a valuable resource for economists and economic theorists.

This book analyses stochastic dynamic systems across a broad spectrum in economics and finance. The major unifying theme is the coherent and rigorous treatment of uncertainty and its implications for describing stochastic processes by the stochastic differential equations of the fundamental models in various fields. Pertinent subjects are interrelated, juxtaposed, and examined for consistency in theoretical and empirical contexts. The volume consists of three parts: Developments in Stochastic Dynamics; Stochastic Dynamics in Basic Economic Growth Models; Intertemporal Optimisation in Consumption, Finance, and Growth. Key topics include: fractional Brownian motion in finance; moment evolution of Gaussian and geometric Wiener diffusions; stochastic kinematics and stochastic mechanics; stochastic growth in continuous time; time delays and Hopf bifurcation; consumption and investment strategies; differential systems in finance and life insurance; uncertainty of technological innovations; investment and employment cycles; stochastic control theory; and risk aversion. The works collected in this book serves to bridge the "old" deterministic dynamics and the "new" stochastic dynamics. The collection is important for scholars and advanced graduate students of economics, statistics, and applied mathematics.

Management in a dynamic process reflected in three essential functions : management of time, change and people. Each of these functions entails problems whose origin can be traced to the special character of time and activities that take place over time. The book provides a bridging gap between quantitative theories imbedded in the systems approach and managerial decision-making over time and under risk. The conventional wisdom that management is a dynamic process is rendered operational. Contents for volume 1 : On time. Planning and planning models - over time. Planning decision - over time. [jaquette].

International Macroeconomic Dynamics provides extensive applications of important macroeconomic dynamic models to the international economy. For a long time, the study of macroeconomics has focused almost exclusively on a closed economy and downplayed the role of international transactions. Today, however, researchers recognize that one cannot fully understand domestic macroeconomic relationships without considering the global economy within which each country operates. Increasingly, economists are treating international transactions as an integral part of the macroeconomic system, and international macroeconomics has become an area of intensive research activity. International Macroeconomic Dynamics provides extensive applications of important macroeconomic dynamic models to the international economy. It adopts the main contemporary macroeconomic framework, the representative agent model, and develops a series of models of increasing complexity. The author considers both small and large economies and analyzes them in both deterministic and stochastic contexts. The emphasis is very much on the development of the analytical models; a novel feature is the extensive use of continuous-time stochastic methods. While the author applies the models to a range of important policy issues, particularly issues of fiscal policy, the reader is invited to view the analyses as blueprints for other applications.