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"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"--