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Medientyp:
Buch
Titel:
Advances in heavy tailed risk modeling
:
a handbook of operational risk
Enthält:
Cover; Title Page; Copyright; Dedication; Contents in Brief; Contents; Preface; Acronyms; Symbols; List of Distributions; Chapter 1 Motivation for Heavy-Tailed Models; 1.1 Structure of the Book; 1.2 Dominance of the Heaviest Tail Risks; 1.3 Empirical Analysis Justifying Heavy-Tailed Loss Models-in OpRisk; 1.4 Motivating Parametric, Spliced and Non-Parametric Severity Models; 1.5 Creating Flexible Heavy-Tailed Models via Splicing; Chapter 2 Fundamentals of Extreme Value Theory for OpRisk; 2.1 Introduction; 2.2 Historical Perspective on EVT and Risk
2.3 Theoretical Properties of Univariate EVT-Block Maxima and the GEV Family2.4 Generalized Extreme Value Loss Distributional Approach (GEV-LDA); 2.4.1 Statistical Considerations for Applicability of the GEV Model; 2.4.2 Various Statistical Estimation Procedures for the GEV Model Parameters in OpRisk Settings; 2.4.3 GEV Sub-Family Approaches in OpRisk LDA Modeling; 2.4.4 Properties of the Frechet-Pareto Family of Severity Models; 2.4.5 Single Risk LDA Poisson-Generalized Pareto Family; 2.4.6 Single Risk LDA Poisson-Burr Family; 2.4.7 Properties of the Gumbel family of Severity Models
2.4.8 Single Risk LDA Poisson-LogNormal Family2.4.9 Single Risk LDA Poisson-Benktander II Models; 2.5 Theoretical Properties of Univariate EVT-Threshold Exceedances; 2.5.1 Understanding the Distribution of Threshold Exceedances; 2.6 Estimation Under the Peaks Over Threshold Approach via the Generalized Pareto Distribution; 2.6.1 Maximum-Likelihood Estimation Under the GPD Model; 2.6.2 Comments on Probability-Weighted Method of Moments Estimation Under the GPD Model; 2.6.3 Robust Estimators of the GPD Model Parameters; 2.6.4 EVT-Random Number of Losses
Chapter 3 Heavy-Tailed Model Class Characterizations for LDA3.1 Landau Notations for OpRisk Asymptotics: Big and Little `Oh'; 3.2 Introduction to the Sub-Exponential Family of Heavy-Tailed Models; 3.3 Introduction to the Regular and Slow Variation Families-of Heavy-Tailed Models; 3.4 Alternative Classifications of Heavy-Tailed Models and Tail Variation; 3.5 Extended Regular Variation and Matuszewska Indices for Heavy-Tailed Models; Chapter 4 Flexible Heavy-Tailed Severity Models: α-Stable Family; 4.1 Infinitely Divisible and Self-Decomposable Loss Random Variables
4.1.1 Basic Properties of Characteristic Functions4.1.2 Divisibility and Self-Decomposability of Loss Random Variables; 4.2 Characterizing Heavy-Tailed α-Stable Severity Models; 4.2.1 Characterisations of α-Stable Severity Models via the Domain of Attraction; 4.3 Deriving the Properties and Characterizations of the α-Stable Severity Models; 4.3.1 Unimodality of α-Stable Severity Models; 4.3.2 Relationship between L Class and α-Stable Distributions; 4.3.3 Fundamentals of Obtaining the α-Stable Characteristic Function
4.3.4 From Lévy-Khinchin's Canonical Representation to the α-Stable Characteristic Function Parameterizations
Beschreibung:
"Covers key mathematical and statistical aspects of the quantitative modelling of heavy tailed loss processes in operational risk and insurance settings. Includes advanced topics on risk modelling in high consequence low frequency loss processes, key aspects of extreme value theory, and classification of different classes of heavy tailed risk process models. Primarily developed for advanced risk management practitioners and quantitative analysts. Suitable as a core reference for an advanced mathematical or statistical risk management masters course or a PhD research course on risk management and asymptotics"--
"A companion book to Fundamental Aspects of Operational Risk Modeling and Insurance Analytics: A Handbook of Operational Risk (2014), this book covers key mathematical and statistical aspects of the quantitative modelling of heavy tailed loss processes in operational risk and insurance settings. This book can add value to the industry by providing clear and detailed coverage of modelling for heavy tailed operational risk losses from both a rigorous mathematical as well as a statistical perspective. Few books cover the range of details provided both the mathematical and statistical features of such models, directly targeting practitioners. The book focuses on providing a sound understanding of how one would mathematically and statistically model, estimate, simulate and validate heavy tailed loss process models in operational risk. Coverage includes advanced topics on risk modelling in high consequence low frequency loss processes. This features splice loss models and motivation for heavy tailed risk processes models. The key aspects of extreme value theory and their development in loss distributional approach modelling is considered. Classification and understanding of different classes of heavy tailed risk process models is discussed, this leads into topics on heavy tailed closed form loss distributional approach models and flexible heavy tailed risk models such as a-stable and tempered stable models. The remainder of the chapters covers advanced topics on risk measures and asymptotics for heavy tailed compound process models. The finishing chapter covers advanced topics including forming links between actuarial compound process recursions and monte carlo numerical solutions for capital and risk measure estimations"--
Covers key mathematical and statistical aspects of the quantitative modelling of heavy tailed loss processes in operational risk and insurance settings. Includes advanced topics on risk modelling in high consequence low frequency loss processes, key aspects of extreme value theory, and classification of different classes of heavy tailed risk process models. Primarily developed for advanced risk management practitioners and quantitative analysts. Suitable as a core reference for an advanced mathematical or statistical risk management masters course or a PhD research course on risk management and asymptotics.
A companion book to Fundamental Aspects of Operational Risk Modeling and Insurance Analytics: A Handbook of Operational Risk (2014), this book covers key mathematical and statistical aspects of the quantitative modelling of heavy tailed loss processes in operational risk and insurance settings. This book can add value to the industry by providing clear and detailed coverage of modelling for heavy tailed operational risk losses from both a rigorous mathematical as well as a statistical perspective. Few books cover the range of details provided both the mathematical and statistical features of such models, directly targeting practitioners. The book focuses on providing a sound understanding of how one would mathematically and statistically model, estimate, simulate and validate heavy tailed loss process models in operational risk. Coverage includes advanced topics on risk modelling in high consequence low frequency loss processes. This features splice loss models and motivation for heavy tailed risk processes models. The key aspects of extreme value theory and their development in loss distributional approach modelling is considered. Classification and understanding of different classes of heavy tailed risk process models is discussed, this leads into topics on heavy tailed closed form loss distributional approach models and flexible heavy tailed risk models such as a-stable and tempered stable models. The remainder of the chapters covers advanced topics on risk measures and asymptotics for heavy tailed compound process models. The finishing chapter covers advanced topics including forming links between actuarial compound process recursions and monte carlo numerical solutions for capital and risk measure estimations.