Bayesian Claims Reserving Methods in Non-life Insurance with Stan An
This book first provides a review of various aspects of Bayesian statistics. It then investigates three types of claims reserving models in the Bayesian framework: chain ladder models, basis expansion models involving a tail factor, and multivariate copul
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Bayesian Claims Reserving Methods in Non-life Insurance with Stan An Introduction
Bayesian Claims Reserving Methods in Non-life Insurance with Stan
Guangyuan Gao
Bayesian Claims Reserving Methods in Non-life Insurance with Stan An Introduction
123
Guangyuan Gao School of Statistics Renmin University of China Beijing, China
ISBN 978-981-13-3608-9 ISBN 978-981-13-3609-6 https://doi.org/10.1007/978-981-13-3609-6
(eBook)
Library of Congress Control Number: 2018963287 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
Bayesian models are very popular in non-life claims reserving. This monograph provides a review of Bayesian claims reserving models and their underlying Bayesian inference theory. It investigates three types of claims reserving models in Bayesian framework: chain ladder models, basis expansion models involving tail factor, and multivariate copula models. One of the core techniques in Bayesian modeling is inferential methods. This monograph largely relies on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes. This monograph has the following three distinguishing features: • It has a thorough review of various aspects of Bayesian statistics and relates them to claims reserving problems. • It addresses three important points in claims reserving: tail development, stochastic version of payments per claim incurred method, and aggregation of liabilities from correlated portfolios. • It provides explicit Stan code for non-life insurance claims reserving. Beijing, China September 2018
Guangyuan Gao
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Acknowledgements
I am very grateful to Borek Pu
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