## Similar

This book is intended to provide students and practitioners the knowledge and theoretical tools they need in order to answer these and other more general questions in the context of so-called environmental finance theory, a new field of research that investigates the economic, financial and managerial impacts of market-based environmental policies.

What is the nature of the relation between economic growth and the environment?

This book intends to provide students and practitioners with the knowledge and the theoretical tools necessary to answer these and other related questions in the context of the so-called environmental finance theory. This is a new research strand that investigates the economic, financial, and managerial impacts of carbon pricing policies.

The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.

Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.

These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.

The Ariadne’s thread leads the reader from Louis Bachelier’s thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavin’s stochastic calculus of variations. The book also features a description of the trainings of French financial analysts which will help them to become experts in these fast evolving mathematical techniques.

- Gaussian subspaces of the Gaussian space of Brownian motion;

- Brownian quadratic funtionals;

- Brownian local times,

- Exponential functionals of Brownian motion with drift;

- Winding number of one or several Brownian motions around one or several points or a straight line, or curves;

- Time spent by Brownian motion below a multiple of its one-sided supremum.

Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance.