Risk Quantification and Allocation Methods for Practitioners

by Jaume Belles-Sampers, Montserrat Guillén and Miguel Santolino

Amsterdam University Press, 2017 eISBN: 978-90-485-3458-6 | Cloth: 978-94-6298-405-9

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC

ABOUT THIS BOOK

Risk Quantification and Allocation Methods for Practitioners offers a practical approach to risk management in the financial industry. This in-depth study provides quantitative tools to better describe qualitative issues, as well as clear explanations of how to transform recent theoretical developments into computational practice, and key tools for dealing with the issues of risk measurement and capital allocation.

AUTHOR BIOGRAPHY

Jaume Belles-Sampers is assistant professor in the Department of Econometrics, Statistics, and Applied Economics at the University of Barcelona, where Montserrat Guillén is professor in the same department and Miguel Santolino is associate professor.

TABLE OF CONTENTS

Preface
Contents
List of Figures
List of Tables
Part I Risk Assessment
1 Preliminary concepts on quantitative risk measurement
1.1 Risk measurement – Theory
1.2 Risk measurement – Practice
1.3 Exercises
2 Data on losses for risk evaluation
2.1 An example on three dimensional data
2.2 Basic graphical analysis of the loss severity distributions
2.3 Quantile estimation
2.4 Examples
3 A family of distortion risk measures
3.1 Overview on risk measures
3.2 Distortion risk measures
3.3 A new family of risk mesures: GlueVaR
3.4 Linear combination of risk measures
3.5 Subadditivity
3.6 Concavity of the distortion function
3.7 Example of risk measurement with GlueVaR
3.8 Exercises
4 GlueVaR and other new risk measures
4.1 Analytical closed-form expressions of GlueVaR
4.2 On the relationship between GlueVaR and Tail Distortion risk measures
4.3 On the relationship between GlueVaR and RVaR risk measures
4.4 Example
4.5 Exercises
5 Risk measure choice
5.1 Aggregate attitude towards risk
5.2 Application of risk assessment in a scenario involving catastrophic losses
5.3 GlueVaR to reflect risk attitudes
5.4 Exercises
Part II Capital Allocation Problems
6 An overview on capital allocation problems
6.1 Main concepts and notation
6.2 Properties of capital allocation principles
6.3 Review of some principles
6.4 Further reading
6.5 Exercises
7 Capital allocation based on GlueVaR
7.1 A capital allocation framework
7.2 The Haircut capital allocation principle
7.3 Proportional risk capital allocation principles using GlueVaR
7.4 An example of risk capital allocation on claim costs
7.5 Exercises
8 Capital allocation principles as compositional data
8.1 The simplex and its vectorial and metric structure
8.2 Simplicial concepts applied to capital allocation
8.3 Exercises
Appendix
A.1 Equivalent expression for the GlueVaR distortion function
A.2 Bijective relationship between heights and weights as parameters for GlueVaR risk measures
A.3 Relationship between GlueVaR and Tail Distortion risk measures
Bibliography
Biographies of the authors
Index

Risk Quantification and Allocation Methods for Practitioners

by Jaume Belles-Sampers, Montserrat Guillén and Miguel Santolino

Amsterdam University Press, 2017 eISBN: 978-90-485-3458-6 Cloth: 978-94-6298-405-9

Risk Quantification and Allocation Methods for Practitioners offers a practical approach to risk management in the financial industry. This in-depth study provides quantitative tools to better describe qualitative issues, as well as clear explanations of how to transform recent theoretical developments into computational practice, and key tools for dealing with the issues of risk measurement and capital allocation.

AUTHOR BIOGRAPHY

Jaume Belles-Sampers is assistant professor in the Department of Econometrics, Statistics, and Applied Economics at the University of Barcelona, where Montserrat Guillén is professor in the same department and Miguel Santolino is associate professor.

TABLE OF CONTENTS

Preface
Contents
List of Figures
List of Tables
Part I Risk Assessment
1 Preliminary concepts on quantitative risk measurement
1.1 Risk measurement – Theory
1.2 Risk measurement – Practice
1.3 Exercises
2 Data on losses for risk evaluation
2.1 An example on three dimensional data
2.2 Basic graphical analysis of the loss severity distributions
2.3 Quantile estimation
2.4 Examples
3 A family of distortion risk measures
3.1 Overview on risk measures
3.2 Distortion risk measures
3.3 A new family of risk mesures: GlueVaR
3.4 Linear combination of risk measures
3.5 Subadditivity
3.6 Concavity of the distortion function
3.7 Example of risk measurement with GlueVaR
3.8 Exercises
4 GlueVaR and other new risk measures
4.1 Analytical closed-form expressions of GlueVaR
4.2 On the relationship between GlueVaR and Tail Distortion risk measures
4.3 On the relationship between GlueVaR and RVaR risk measures
4.4 Example
4.5 Exercises
5 Risk measure choice
5.1 Aggregate attitude towards risk
5.2 Application of risk assessment in a scenario involving catastrophic losses
5.3 GlueVaR to reflect risk attitudes
5.4 Exercises
Part II Capital Allocation Problems
6 An overview on capital allocation problems
6.1 Main concepts and notation
6.2 Properties of capital allocation principles
6.3 Review of some principles
6.4 Further reading
6.5 Exercises
7 Capital allocation based on GlueVaR
7.1 A capital allocation framework
7.2 The Haircut capital allocation principle
7.3 Proportional risk capital allocation principles using GlueVaR
7.4 An example of risk capital allocation on claim costs
7.5 Exercises
8 Capital allocation principles as compositional data
8.1 The simplex and its vectorial and metric structure
8.2 Simplicial concepts applied to capital allocation
8.3 Exercises
Appendix
A.1 Equivalent expression for the GlueVaR distortion function
A.2 Bijective relationship between heights and weights as parameters for GlueVaR risk measures
A.3 Relationship between GlueVaR and Tail Distortion risk measures
Bibliography
Biographies of the authors
Index