Mario V. Wüthrich

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.

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.

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.

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.