A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time. Helps to answer the question: which risk measure is best for a given problem? Finds new relations between existing classes of risk measures Describes applications in finance and extends them where possible Presents the theory of probability metrics in a more accessible form which would be appropriate for non-specialists in the field Applications include optimal portfolio choice, risk theory, and numerical methods in finance Topics requiring more mathematical rigor and detail are included in technical appendices to chapters

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization The finance industry is seeing increased interest in new risk measures and techniques for portfolio optimization when parameters of the model are uncertain. This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers. They also clearly show how stochastic models, risk assessment, and optimization are essential to mastering risk, uncertainty, and performance measurement. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization provides quantitative portfolio managers (including hedge fund managers), financial engineers, consultants, and academic researchers with answers to the key question of which risk measure is best for any given problem.

This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.

"This book, Measuring Market Risk with Value at Risk by Vipul Bansal and Pietro Penza, has three advantages over earlier works on the subject. First, it takes a decidedly global approach-an essential ingredient for any comprehensive work on market risk. Second, it ties the scientifically grounded, yet intuitively appealing, VaR measure to earlier, more idiosyncratic measures of market risk that are used in specific market environs (e.g., duration in fixed income). Finally, it encompasses all of the accepted approaches to calculating a VaR measure and presents them in a clearly explained fashion with supporting illustrations and completely worked-out examples." -from the Foreword by John F. Marshall, PhD, Principal, Marshall, Tucker & Associates, LLC "Measuring Market Risk with Value at Risk offers a much-needed intellectual bridge, a translation from the esoteric realm of mathematical finance to the domain of financial managers who seek guidance in applying developments from this important field of research as well as that of MBA-level graduate instruction. I believe the authors have done a commendable job of providing a carefully crafted, highly readable, and most useful work, and intend to recommend it to all those involved in business risk management applications." -Anthony F. Herbst, PhD, Professor of Finance and C.R. and D.S. Carter Chair, The University of Texas, El Paso and Founding editor of The Journal of Financial Engineering (1991-1998) "Finally there's a book that strikes a balance between rigor and application in the area of risk management in the banking industry. This innovative book is a MUST for both novices and professionals alike." -Robert P. Yuyuenyongwatana, PhD, Associate Professor of Finance, Cameron University "Measuring Market Risk with Value at Risk is one of the most complete discussions of this emerging topic in finance that I have seen. The authors develop a logical and rigorous framework for using VaR models, providing both historical references and analytical applications." -Kevin Wynne, PhD, Associate Professor of Finance, Lubin School of Business, Pace University

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)