A Probability Metrics Approach to Financial Risk Measures

1. Auflage 2011
ISBN: 978-1-4051-8369-7
Verlag: Wiley

Buch, Englisch, 392 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 719 g

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

Autoren/Hrsg.

Rachev, Svetlozar T

Stoyanov, Stoyan V

Fabozzi, Frank J

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Unternehmensfinanzierung
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Bankwirtschaft
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Anlagen & Wertpapiere
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Börse, Rohstoffe
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensfinanzen Finanzierung, Investition, Leasing

Inhaltsverzeichnis

Chapter 1 Introduction.

1.1 Probability metrics.

1.2 Applications in finance.

Chapter 2 Probability distances and metrics.

2.1 Introduction.

2.2 Some examples of probability metrics.

2.3 Distance and semidistance spaces.

2.4 Definitions of probability distances and metrics.

2.5 Summary.

2.6 Technical appendix.

Chapter 3 Choice under uncertainty.

3.1 Introduction.

3.2 Expected utility theory.

3.3 Stochastic dominance.

3.4 Probability metrics and stochastic dominance.

3.5 Cumulative Prospect Theory.

3.6 Summary.

3.7 Technical appendix.

Chapter 4 A classification of probability distances.

4.1 Introduction.

4.2 Primary distances and primary metrics.

4.3 Simple distances and metrics.

4.4 Compound distances and moment functions.

4.5 Ideal probability metrics.

4.6 Summary.

4.7 Technical appendix.

Chapter 5 Risk and uncertainty.

5.1 Introduction.

5.2 Measures of dispersion.

5.3 Probability metrics and dispersion measures.

5.4 Measures of risk.

5.5 Risk measures and dispersion measures.

5.6 Risk measures and stochastic orders.

5.7 Summary.

5.8 Technical appendix.

Chapter 6 Average value-at-risk.

6.1 Introduction.

6.2 Average value-at-risk.

6.2.1 AVaR for stable distributions.

6.3 AVaR estimation from a sample.

6.4 Computing portfolio AVaR in practice.

6.5 Back-testing of AVaR.

6.6 Spectral risk measures.

6.7 Risk measures and probability metrics.

6.8 Risk measures based on distortion functionals.

6.9 Summary.

6.10 Technical appendix.

Chapter 7 Computing AVaR through Monte Carlo.

7.1 Introduction.

7.2 An illustration of Monte Carlo variability.

7.3 Asymptotic distribution, classical conditions.

7.4 Rate of convergence to the normal distribution.

7.5 Asymptotic distribution, heavy-tailed returns.

7.6 Rate of convergence, heavy-tailed returns.

7.7 On the choice of a distributional model.

7.8 Summary.

7.9 Technical appendix.

Chapter 8 Stochastic dominance revisited.

8.1 Introduction.

8.2 Metrization of preference relations.

8.3 The Hausdorff metric structure.

8.4 Examples.

8.5 Utility-type representations.

8.6 Almost stochastic orders and degree of violation.

8.7 Summary.

8.8 Technical appendix.

Über Autor(innen)

Svetlozar (Zari) T. Rachev is Chair-Professor in Statistics, Econometrics and Mathematical Finance at the University of Karlsruhe in the School of Economics and Business Engineering. He is also Professor Emeritus at the University of California, Santa Barbara in the Department of Statistics and Applied Probability. He has published seven monographs, eight handbooks and special-edited volumes, and over 300 research articles. His recently coauthored books published by Wiley in mathematical finance and financial econometrics include Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio selection, and Option Pricing (2005), Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis (2007), Financial Econometrics: From Basics to Advanced Modeling Techniques (2007), and Bayesian Methods in Finance (2008). He is cofounder of Bravo Group, now FinAnalytica, specializing in financial risk-management software, for which he serves as Chief Scientist.

Stoyan V. Stoyanov, Ph.D. is the Head of Quantitative Research at FinAnalytica specializing in financial risk management software. He is author and co-author of numerous papers some of which have recently appeared in Economics Letters, Journal of Banking and Finance, Applied Mathematical Finance, Applied Financial Economics, and International Journal of Theoretical and Applied Finance. He is a coauthor of the mathematical finance book Advanced Stochastic Models, Risk Assessment and Portfolio Optimization: the Ideal Risk, Uncertainty and Performance Measures (2008) published by Wiley. Dr. Stoyanov has years of experience in applying optimal portfolio theory and market risk estimation methods when solving practical problems of clients of FinAnalytica.

Frank J. Fabozzi is Professor in the Practice of Finance in the School of Management at Yale University. Prior to joining the Yale faculty, he was a Visiting Professor of Finance in the Sloan School at MIT. Professor Fabozzi is a Fellow of the International Center for Finance at Yale University and on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University. He is the editor of the Journal of Portfolio Management. His recently coauthored books published by Wiley in mathematical finance and financial econometrics include The Mathematics of Financial Modeling and Investment Management (2004), Financial Modeling of the Equity Market: From CAPM to Cointegration (2006), Robust Portfolio Optimization and Management (2007), Financial Econometrics: From Basics to Advanced Modeling Techniques (2007), and Bayesian Methods in Finance (2008).