Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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

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Quantitative Risk Management: Concepts, Techniques, and Tools

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

A first course in stochastic processes

This focuses on models and data that arise from repeated observations of a cross-section of individuals, households or companies. These models have found important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented graduate social science students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also describes substantive applications from across the social sciences, showing the breadth and scope that these models enjoy. The applications are enhanced by real-world data sets and software programs in SAS and Stata.

Longitudinal and Panel Data: Analysis and Applications in the Social Sciences

A fully time-continuous approach is taken to the problem of predicting the total liability of a non-hfe insurance company Claims are assumed to be generated by a non-homogeneous marked Polsson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Polsson processes By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner Special attention ~s gwen to the case where the claim Intensity per risk unit IS a stationary stochastic process. A theory of continuous linear pre&ctlon ~s mstrumental.

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Prediction of Outstanding Liabilities in Non-Life Insurance

Power tailed ruin probabilities in the presence of risky investments

Ruin problems with assets and liabilities of diffusion type

Thas as a follow-up of a previous paper by the author, where claims reserving m non-hfe insurance as treated in the framework of a marked Polsson claims process A key result on decomposmon of the process as generahzed, and a number of related results are added. Their usefulness is demonstrated by examples and, in pamcular, the connection to the analogous discrete tame model is clarified. The problem of predmtmg the outstanding part of reported but not settled clmms is revisated and, by way of example, solved in a model where the partml payments are governed by a Dmchlet process The process of reported clmms is examined, and ats dual relationship to the process of occurred claims is pointed out.

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Prediction of Outstanding Liabilities II. Model Variations and Extensions

Prospective and retrospective reserves are defined as conditional expected values, given some information available at the time of consideration. Each specification of the information invoked gives rise to a corresponding pair of reserves. Relationships between reserves are established in the general set-up. For the prospective reserve the present definition conforms with, and generalizes, the traditional one. For the retrospective reserve it appears to be novel. Special attention is given to the continuous time Markov chain model frequently used in the context of life and pension insurance. Thiele’s differential equation for the prospective reserve is shown to have a retrospective counterpart. It is pointed out that the prospective and retrospective differential equations have, respectively, the Kolmogorov backward and forward differential equations as special cases. Practical uses of the differential equations are demonstrated by examples.

Ragnar Norberg

Papers

Prediction of Outstanding Liabilities in Non-Life Insurance

Power tailed ruin probabilities in the presence of risky investments

Ruin problems with assets and liabilities of diffusion type

Prediction of Outstanding Liabilities II. Model Variations and Extensions

Reserves in Life and Pension Insurance