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AbstractWe present a claims reserving technique that uses claim-specific feature and past payment information in order to estimate claims reserves for individual reported claims. We design one single neural network allowing us to estimate expected future cash flows for every individual reported claim. We introduce a consistent way of using dropout layers in order to fit the neural network to the incomplete time series of past individual claims payments. A proof of concept is provided by applying this model to synthetic as well as real insurance data sets for which the true outstanding payments for reported claims are known.

Data -- Deterministic reserving methods -- Stochastic reserving methods -- Reserving in practice -- Selected additional reserving topics -- Reserving in specific contexts

"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.

Actuaries working in claims reserving are often faced, among others, with the following two tasks: the prediction of future outstanding loss liabilities, as well as the quantification of their risk. Within claims reserving there exist various methods in which vagueness and subjective judgement is often not considered. A formal approach is given e.g. by fuzzy set theory. Besides an overview of applications of fuzzy set theory in claims reserving the author presents three ways of how subjective assessment can be implemented in the chain-ladder as well as the Bornhuetter Ferguson method.

Acknowledgements; Contents; List of Figures; List of Tables; List of Symbols; List of Abbreviations; 1 | Introduction; 2 | Fuzzy Theory; 3 | Applications of Fuzzy Theory in Insurance; 4 | Methods of Claims Reserving; 5 | The Fuzzy Chain-Ladder Model -- An Approach with Fuzzy Numbers; 6 | Another Fuzzy Chain-Ladder Model -An Application of Fuzzy Regression Techniques; 7 | The Fuzzy Bornhuetter Ferguson Method; 8 | Conclusion; A | Statistical Basics; Zusammenfassung; Summary; Bibliography.