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This book examines the role of applied and theoretical mathematics in various areas of international business. These include the trade of goods, services, technology, capital and/or knowledge.

The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or U.S. Government. ; This report contains project summaries of the research projects in the Department of Applied Mathematics. A list ofrecent publications is also included, which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. Thesis abstracts of students advised by faculty in the Department are also included.

"The book covers the essential mathematics behind topics including quantum cognition, option pricing, and quantum game theory, and delves into the nuts and bolts of quantum mechanics, the principles of quantum economic modelling, and the basics of quantum computer logic. On the way the reader will learn how quantum interference can be used to model cognitive dissonance, how a quantum walk goes further than a random walk, and how financial entanglement explains the rate of mortgage default. It is aimed at anyone who wants to understand the quantum ideas working their way into economics and finance, without getting drowned in wave equations."

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and deterministic setting. We derive rigorously the first order optimality conditions useful for numerical computation of mean field optimal controls. We introduce a novel approximating hierarchy of sub-optimal controls based on a Boltzmann approach, whose computation requires a very moderate numerical complexity with respect to the one of the optimal control. We provide numerical experiments for models in opinion formation comparing the behavior of the control hierarchy. ; ERC advanced Grant 668998 (OCLOC) ; (VLID)2523620

AbstractThe power of the symbolic mathematics program Maple is demonstrated for teaching topics from microeconomics (the benefits of portfolio diversification) and econometrics (a geometric perspective of multicollinearity). In particular, it appears that the use of symbolic mathematics programs has excellent potential to strengthen the development and integration of graphical and algebraic intuition for a wide variety of economic problems.