Book•
Mixed Poisson Processes
01 May 1997-
TL;DR: In this paper, the Mixed Poisson Distributions (MPD) is defined as a mixture of Cox Processes, Gauss-Poisson Processes and Mixed Renewal Processes.
Abstract: Preface Introduction The Mixed Poisson Distributions Some Basic Concepts The Mixed Poisson Process Some Related Processes Cox Processes Gauss-Poisson Processes Mixed Renewal Processes Characterization of Mixed Poisson Processes Reliability Properties of Mixed Poisson Processes Characterization within Birth Processes Characterization within Stationary Point Processes Characterization within General Point Processes Compound Mixed Poisson Distributions Compound Distributions Exponential Bounds Asymptotic Behaviour Recursive Evaluation The Risk Business The Claim Process Ruin Probabilities
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TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.
Abstract: (2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.
2,729 citations
Book•
16 Oct 2005
TL;DR: The most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management can be found in this paper, where the authors describe the latest advances in the field, including market, credit and operational risk modelling.
Abstract: This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation
2,580 citations
Book•
25 Aug 2008
TL;DR: Models and Frameworks for Analysis of Recurrent Events based on Counts and Rate Functions and Analysis of Gap Times are presented.
Abstract: Models and Frameworks for Analysis of Recurrent Events.- Methods Based on Counts and Rate Functions.- Analysis of Gap Times.- General Intensity-Based Models.- Multitype Recurrent Events.- Observation Schemes Giving Incomplete or Selective Data.- OtherTopics.
692 citations
TL;DR: A treatment of the mathematical properties is provided for the Lindley distribution, which includes moments, cumulants, characteristic function, failure rate function, mean residual life function, and mean deviations.
541 citations
TL;DR: In this paper, the authors dealt mainly with the application of financial pricing techniques to insurance problems, and presented that realistic models for asset price processes are typically incomplete, and that actuarial concepts for risk-management might prove helpful in dealing with these “unhedgeable” risks.
Abstract: Publisher Summary This chapter dealt mainly with the application of financial pricing techniques to insurance problems. However, actuarial concepts are also of increasing relevance for finance problems. This chapter presents that realistic models for asset price processes are typically incomplete. Actuarial concepts for risk-management might prove helpful in dealing with these “unhedgeable” risks. An example where such concepts are already applied, is the RAC-(risk adjusted capital) approach in insurance that has become popular among investment banks as a tool for the determination of risk capital and capital allocations. It is no coincidence that Swiss Bank Cooperation (now UBS) called one of its credit risk management systems ACRA, which stands for Actuarial Credit Risk Accounting.
421 citations