Michael Merz

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.

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.

Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments in this area in the financial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wüthrich combine ideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fully consistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options, dividend to shareholder questions, the role of re-insurance, etc. This work embeds the solvency discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in the financial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a good background in probability theory and statistics, and should be familiar with popular distributions, stochastic processes, martingales, etc.

Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments in this area in the financial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wüthrich combine ideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fully consistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options, dividend to shareholder questions, the role of re-insurance, etc. This work embeds the solvency discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in the financial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a good background in probability theory and statistics, and should be familiar with popular distributions, stochastic processes, martingales, etc.

Die Nordrhein-Westf lische Akademie der Wissenschaften und der K nste ist eine Vereinigung der f hrenden Forscherinnen und Forscher des Landes. Sie wurde 1970 als Nachfolgeeinrichtung der Arbeitsgemeinschaft f r Forschung des Landes Nordrhein-Westfalen gegr ndet. Die Akademie ist in drei wissenschaftliche Klassen f r Geisteswissenschaften, f r Naturwissenschaften und Medizin sowie f r Ingenieur- und Wirtschaftswissenschaften und in eine Klasse der K nste gegliedert. Mit Publikationen zu den wissenschaftlichen Vortr gen in den Klassensitzungen, zu ffentlichen Veranstaltungen und Symposien will die Akademie die Fach- und allgemeine ffentlichkeit ber die Arbeiten der Akademie und ihrer Forschungsstellen informieren.

Claims reserving is central to the insurance industry. Insurance liabilities depend on a number of different risk factors which need to be predicted accurately. This prediction of risk factors and outstanding loss liabilities is the core for pricing insurance products, determining the profitability of an insurance company and for considering the financial strength (solvency) of the company. Following several high-profile company insolvencies, regulatory requirements have moved towards a risk-adjusted basis which has lead to the Solvency II developments. The key focus in the new regime is that financial companies need to analyze adverse developments in their portfolios. Reserving actuaries now have to not only estimate reserves for the outstanding loss liabilities but also to quantify possible shortfalls in these reserves that may lead to potential losses. Such an analysis requires stochastic modeling of loss liability cash flows and it can only be done within a stochastic framework. Therefore stochastic loss liability modeling and quantifying prediction uncertainties has become standard under the new legal framework for the financial industry. This book covers all the mathematical theory and practical guidance needed in order to adhere to these stochastic techniques. Starting with the basic mathematical methods, working right through to the latest developments relevant for practical applications; readers will find out how to estimate total claims reserves while at the same time predicting errors and uncertainty are quantified. Accompanying datasets demonstrate all the techniques, which are easily implemented in a spreadsheet. A practical and essential guide, this book is a must-read in the light of the new solvency requirements for the whole insurance industry.

Diese Arbeit wurde mit dem SCOR-Preis fur Aktuarwissenschaften ausgezeichnet. Die risikogerechte Pramienberechnung ist zum einen ein Gebot der Beitragsgerechtigkeit und bewirkt zum anderen eine Verringerung des Moral Hazard Effekts. Daruber hinaus ist die risikoadaquate Pramie der wettbewerbsbeste Preis. Gegenstand dieser Arbeit ist die zum Zweck der risikogerechten Pramienkalkulation entwickelte Credibility-Theorie. Das Ergebnis ist eine konsistente Credibility-Theorie fur eine Betrachtung in diskreter und kontinuierlicher Zeit. Fur die beiden resultierenden allgemeinen Credibility-Modelle in diskreter und in kontinuierlicher Zeit wird gezeigt, wie sich daraus sowohl bekannte als auch neue diskrete Credibility-Modelle und -Schatzer als Spezialfalle ergeben bzw. neue stetige Credibility-Modelle und -Schatzer mit und ohne diskretes Analogon als Spezialfalle ableiten lassen. Fur alle Credibility-Schatzer werden Rekursionsbeziehungen hergeleitet und ihre statistischen Eigenschaften untersucht.

Das Internet stellt zunehmend auch ein Medium zur Abwicklung von Geschaftsprozessen dar. Die Unterstutzung solcher Handelstransaktionen wird unter dem Begriff "Electronic Commerce" zusammengefasst. Dieses Buch zeigt, wie eine Softwareplattform gestaltet sein sollte, die Anforderungen von Nachfragern und Anbietern kommerzieller Softwarekomponenten effizient unterstutzt. Hierbei leitet sich der Softwareentwurf unmittelbar aus der mikrookonomischen Marktdefinition ab. Insbesondere Fragen der Transaktionskostenreduktion und der Innovationsfahigkeit der Marktsoftware fuhren zum Modell eines Elektronischen Dienstemarktes. Bestehende Realisierungsverfahren zur Kooperation in verteilten Systemen werden hinsichtlich ihrer Vereinbarkeit mit diesem Dienstemarkt evaluiert, und es werden neue Verfahren und ihre Integration vorgestellt.