Weak Viability

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.

Bilingual Dictionary of Terms Banks. Finances. Money. Financial Markets / Banques. Finances. Monnaie. Marchés Financiers METODES Editions Collection Culture & Savoir (C&S) François Elandi This bilingual work, fruit of a team of specialists and professionals, deals with banking, finance, and stock market practices with —— more than 25,000 words and terms used in French and in British and North American English of today; —— convenient examples to better assimilate the terms used, contributing to make the work the most precise reference in its specialty; and —— a cross-reference system to more precise definitions and complementary expressions to other words and terms inside the development of a word or an expression. It is intended for ——high school pupils and students of higher education, ——professional users, and ——the general public. In order for them to ——acquire and develop their professional lexicological heritage; ——master the exact terminology in the practice linked to their activity or profession; ——perfect their knowledge in banking, finance, and stock exchange practice; and ——better communicate efficiently. Cet ouvrage bilingue, fruit d’une équipe de spécialistes et de professionnels, traite des pratiques bancaires, financières et boursières, avec : ——Plus de 25000 mots et termes utilisés en français et en anglais britannique et nordaméricain ; ——Des exemples pratiques pour mieux assimiler l’emploi de ces termes, contribuant à faire de l’ouvrage la référence la plus précise dans sa spécialité ; ——Un système de renvois à des définitions et explications complémentaires et plus précises à d’autres mots et termes au sein du développement d’un mot ou d’une expression. Il est destiné : ——A l’élève des lycées et collèges ou à l’étudiant de l’enseignement supérieur ; ——A l’utilisateur professionnel ; ——Au grand public. Pour : ——Acquérir et développer son patrimoine lexicologique professionnel ; ——Maîtriser la terminologie exacte dans la pratique liée à son activité ou à sa profession ; ——Perfectionner ses connaissances dans la pratique bancaire, financière et boursière ; ——Mieux communiquer efficacement.

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"The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." —Bulletin of the AMS "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." —Mededelingen van het Wiskundig Genootschap

An attempt to revitalize the traditions of nonmarket clearing approaches to macroeconomics. Using tools from dynamic analysis, the text introduces a consistent, integrated framework for disequilibrium macroeconomic dynamics and explore its relationship to the competing equilibrium dynamics.

The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style