Probability Distributions In Risk Management Operations

This book is about the formulations, theoretical investigations, and practical applications of new stochastic models for fundamental concepts and operations of the discipline of risk management. It also examines how these models can be useful in the descriptions, measurements, evaluations, and treatments of risks threatening various modern organizations. Moreover, the book makes clear that such stochastic models constitute very strong analytical tools which substantially facilitate strategic thinking and strategic decision making in many significant areas of risk management. In particular the incorporation of fundamental probabilistic concepts such as the sum, minimum, and maximum of a random number of continuous, positive, independent, and identically distributed random variables in the mathematical structure of stochastic models significantly supports the suitability of these models in the developments, investigations, selections, and implementations of proactive and reactive risk management operations. The book makes extensive use of integral and differential equations of characteristic functions, mainly corresponding to important classes of mixtures of probability distributions, as powerful analytical tools for investigating the behavior of new stochastic models suitable for the descriptions and implementations of fundamental risk control and risk financing operations. These risk treatment operations very often arise in a wide variety of scientific disciplines of extreme practical importance.

This concise book for practitioners presents the statistical analysis of operational risk, which is considered the most relevant source of bank risk, after market and credit risk. The book shows that a careful statistical analysis can improve the results of the popular loss distribution approach. The authors identify the risk classes by applying a pooling rule based on statistical tests of goodness-of-fit, use the theory of the mixture of distributions to analyze the loss severities, and apply copula functions for risk class aggregation. Lastly, they assess operational risk data in order to estimate the so-called capital-at-risk that represents the minimum capital requirement that a bank has to hold. The book is primarily intended for quantitative analysts and risk managers, but also appeals to graduate students and researchers interested in bank risks.

A graduate level textbook on probabilistic risk analysis, aimed at statisticians, operations researchers and engineers.

Written by an experienced academic and practitioner, Operational Risk Management fills a gap in the information available on the Basel 2 Accord and offers valuable insights into the nature of operational risk.

Using real-life examples from the banking and insurance industries, Quantitative Operational Risk Models details how internal data can be improved based on external information of various kinds. Using a simple and intuitive methodology based on classical transformation methods, the book includes real-life examples of the combination of internal dat

Foundations of Risk Analysis presents the issues core to risk analysis – understanding what risk means, expressing risk, building risk models, addressing uncertainty, and applying probability models to real problems. The author provides the readers with the knowledge and basic thinking they require to successfully manage risk and uncertainty to support decision making. This updated edition reflects recent developments on risk and uncertainty concepts, representations and treatment. New material in Foundations of Risk Analysis includes: An up to date presentation of how to understand, define and describe risk based on research carried out in recent years. A new definition of the concept of vulnerability consistent with the understanding of risk. Reflections on the need for seeing beyond probabilities to measure/describe uncertainties. A presentation and discussion of a method for assessing the importance of assumptions (uncertainty factors) in the background knowledge that the subjective probabilities are based on A brief introduction to approaches that produce interval (imprecise) probabilities instead of exact probabilities. In addition the new version provides a number of other improvements, for example, concerning the use of cost-benefit analyses and the As Low As Reasonably Practicable (ALARP) principle. Foundations of Risk Analysis provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty.

This book proposes a uniform logic and probabilistic (LP) approach to risk estimation and analysis in engineering and economics. It covers the methodological and theoretical basis of risk management at the design, test, and operation stages of economic, banking, and engineering systems with groups of incompatible events (GIE). This edition includes new chapters providing a detailed treatment of scenario logic and probabilistic models for revealing bribes. It also contains clear definitions and notations, revised sections and chapters, an extended list of references, and a new subject index, as well as more than a hundred illustrations and tables which motivate the presentation.