Advances in heavy tailed risk modeling : a handbook of operational risk / / Gareth W. Peters, Pavel V. Shevchenko

• Record Nr.: UNINA9910821981903321
• Autore: Peters Gareth W. <1978->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2015; ©2015
• ISBN: 1-118-90954-2; 1-118-90956-9
• Edizione: [1st edition]
• Descrizione fisica: 1 online resource (662 p.)
• Collana: Wiley Handbooks in Financial Engineering and Econometrics
• Classificazione: MAT029000TEC009060BUS004000
• Disciplina: 658.15/5
• Soggetti: Risk management; Operational risk
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk pro