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This is the third edition of this well-received textbook, presenting powerful methods for measuring insurance liabilities and assets in a consistent way, with detailed mathematical frameworks that lead to market-consistent values for liabilities. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency. Including updates on recent developments and regulatory changes under Solvency II, this new edition of Market-Consistent Actuarial Valuation also elaborates on different risk measures, providing a revised definition of solvency based on industry practice, and presents an adapted valuation framework which takes a dynamic view of non-life insurance reserving risk

"It is astonishing that the methods used for claims reserving in non life-insurance are, even still today, driven by a deterministic understanding of one or several computational algorithms. Stochastic Claims Reserving Methods in Insurance is tremendously widening this traditional understanding. In this text reserving is model driven, computational algorithms become a consequence of the chosen model. Only with this approach it makes sense to ask how predicted reserves might vary. Stochastic reserving is hence the corner stone of successful risk management for the technical result of an insurance company. Mario Wüthrich and Michael Merz have to be congratulated for opening the eyes of the non-life-actuary to a new and modern dimension." -Hans Bühlmann, Swiss Federal Institute of Technology, Zurich "Assessing the best estimate of insurance liabilities and modelling their adverse developments are among the new frontiers of insurance under the new IAS and the proposed new solvency regimes. This book makes a leap towards these frontiers. The variegated issue of predicting outstanding loss liabilities in non-life insurance is addressed using the unified framework of theory of stochastic processes. The proposed approach provides valuable tools for tackling one of the most challenging forecasting problems in insurance." -Franco Moriconi, Professor of Finance, University of Perugia.

This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus.

Hauptbeschreibung: Prof. Dr. Michael Merz ist Inhaber des Lehrstuhls für Mathematik und Statistik in den Wirtschaftswissenschaften an der Universität Hamburg. Prof. Dr. Mario V. Wüthrich forscht und lehrt am Department für Mathematik der ETH Zürich. Aus dem Inhalt: - Mathematische Grundlagen - Lineare Algebra - Matrizentheorie - Folgen und Reihen - Reellwertige Funktionen in einer und mehreren Variablen - Differential- und Integralrechnung - Optimierung mit und ohne Nebenbedingungen - Numerische Verfahren Die Mathematikausbildun

AbstractIn general insurance, claims are often lower-truncated and right-censored because insurance contracts may involve deductibles and maximal covers. Most classical statistical models are not (directly) suited to model lower-truncated and right-censored claims. A surprisingly flexible family of distributions that can cope with lower-truncated and right-censored claims is the class of MBBEFD distributions that originally has been introduced by Bernegger (ASTIN Bulletin 27(1):99–111, 1997) for reinsurance pricing, but which has not gained much attention outside the reinsurance literature. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class. We show that this class contains both types of densities, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. In addition, we discuss how changes in the deductible or the maximal cover affect the chosen distributions.

Abstract
A statistical analysis which provides a risk assessment of nuclear safety based on historical data is conducted. Classical probabilistic models from risk theory are used to analyze data on nuclear power accidents from 1952 to 2011. Findings are that the severities of nuclear power accidents should be modeled with an infinite mean model and, thus, cannot be insured by an unlimited cover.