A Class of Mixture of Experts Models for General Insurance
A Class of Mixture of Experts Models for General Insurance

Author: Tsz Chai Fung

Publisher:

Published: 2019

Total Pages: 0

ISBN-13:

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In the Property and Casualty (P&C) ratemaking process, it is critical to understand the effect of policyholders' risk profile to the number and amount of claims, the dependence among various business lines and the claim distributions. To include all the above features, it is essential to develop a regression model which is flexible and theoretically justified. Motivated by the issues above, we propose a class of logit-weighted reduced mixture of experts (LRMoE) models for multivariate claim frequencies or severities distributions. LRMoE is interpretable, as it has two components: Gating functions, which classify policyholders into various latent sub-classes; and Expert functions, which govern the distributional properties of the claims. Also, upon the development of denseness theory in regression setting, we show that LRMoE can be fully flexible to capture any distributional, dependence and regression structures. Further, the mathematical tractability of the LRMoE is guaranteed since it satisfies various marginalization and moment properties. Finally, we discuss some special choices of expert functions that make the corresponding LRMoE fully flexible. In the subsequent paper (Fung et al. 2018a), we will focus on the estimation and application aspects of the LRMoE.

A Class of Mixture of Experts Models for General Insurance Ratemaking and Reserving
A Class of Mixture of Experts Models for General Insurance Ratemaking and Reserving

Author: Tsz Chai Fung

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

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Understanding the effect of policyholders' risk profile on the number and the amount of claims, as well as the dependence among different types of claims, are critical to insurance ratemaking and IBNR-type reserving. To accurately quantify such features, it is essential to develop a regression model which is flexible, interpretable and statistically tractable. In this thesis, we first propose a highly flexible nonlinear regression model, namely the logit-weighted reduced mixture of experts (LRMoE) models, for multivariate claim frequencies or severities distributions. The LRMoE model is interpretable as it has two components: Gating functions to classify policyholders into various latent sub-classes and Expert functions to govern the distributional properties of the claims. The model is also flexible to fit any types of claim data accurately and hence minimize the issue of model selection. Model implementation is then illustrated in two ways using a real automobile insurance dataset from a major European insurance company. We first fit the multivariate claim frequencies using an Erlang count expert function. Apart from showing excellent fitting results, we can interpret the fitted model in an insurance perspective and visualize the relationship between policyholders' information and their risk level. We further demonstrate how the fitted model may be useful for insurance ratemaking. The second illustration deals with insurance loss severity data that often exhibits heavy-tail behavior. Using a Transformed Gamma expert function, our model is applicable to fit the severity and reporting delay components of the dataset, which is ultimately shown to be useful and crucial for an adequate prediction of IBNR reserve. After that, we further extend the fitting algorithm to efficiently fit the LRMoE to random censored and truncated regression data. Such an extended algorithm is then found useful and important for broader actuarial applications such as unbiased claim reporting delay modeling and deductible ratemaking.

A Class of Mixture of Experts Models for General Insurance
A Class of Mixture of Experts Models for General Insurance

Author: Tsz Chai Fung

Publisher:

Published: 2019

Total Pages: 0

ISBN-13:

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This paper focuses on the estimation and application aspects of the Erlang Count Logit-weighted Reduced Mixture of Experts model (EC-LRMoE), which is a fully flexible multivariate insurance claim frequency regression model proposed in Fung et al. (2018a). We first prove the identifiability property of the proposed model to ensure that it is a suitable candidate for statistical inference. An Expectation-Conditional-Maximization (ECM) algorithm is developed for efficient model calibrations. Three simulation studies are performed so that the effectiveness of the proposed ECM algorithm and the versatility of the proposed model can be examined. The applicability of the EC-LRMoE is shown through fitting an European automobile insurance dataset. Since the dataset contains several complex features, we find it necessary to adopt such a flexible model. Apart from showing excellent fitting results, we are able to interpret the fitted model in an insurance perspective and to visualize the relationship between policyholders' information and their risk level. Finally, we demonstrate how the fitted model may be useful for insurance ratemaking.

Statistical Foundations of Actuarial Learning and its Applications
Statistical Foundations of Actuarial Learning and its Applications

Author: Mario V. Wüthrich

Publisher: Springer Nature

Published: 2022-11-22

Total Pages: 611

ISBN-13: 303112409X

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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.

Index to IEEE Publications
Index to IEEE Publications

Author: Institute of Electrical and Electronics Engineers

Publisher:

Published: 1996

Total Pages: 1316

ISBN-13:

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Issues for 1973- cover the entire IEEE technical literature.

Loss Models
Loss Models

Author: Stuart A. Klugman

Publisher: John Wiley & Sons

Published: 2012-01-25

Total Pages: 758

ISBN-13: 0470391332

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An update of one of the most trusted books on constructing and analyzing actuarial models Written by three renowned authorities in the actuarial field, Loss Models, Third Edition upholds the reputation for excellence that has made this book required reading for the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) qualification examinations. This update serves as a complete presentation of statistical methods for measuring risk and building models to measure loss in real-world events. This book maintains an approach to modeling and forecasting that utilizes tools related to risk theory, loss distributions, and survival models. Random variables, basic distributional quantities, the recursive method, and techniques for classifying and creating distributions are also discussed. Both parametric and non-parametric estimation methods are thoroughly covered along with advice for choosing an appropriate model. Features of the Third Edition include: Extended discussion of risk management and risk measures, including Tail-Value-at-Risk (TVaR) New sections on extreme value distributions and their estimation Inclusion of homogeneous, nonhomogeneous, and mixed Poisson processes Expanded coverage of copula models and their estimation Additional treatment of methods for constructing confidence regions when there is more than one parameter The book continues to distinguish itself by providing over 400 exercises that have appeared on previous SOA and CAS examinations. Intriguing examples from the fields of insurance and business are discussed throughout, and all data sets are available on the book's FTP site, along with programs that assist with conducting loss model analysis. Loss Models, Third Edition is an essential resource for students and aspiring actuaries who are preparing to take the SOA and CAS preliminary examinations. It is also a must-have reference for professional actuaries, graduate students in the actuarial field, and anyone who works with loss and risk models in their everyday work. To explore our additional offerings in actuarial exam preparation visit www.wiley.com/go/actuarialexamprep.

Non-Life Insurance Pricing with Generalized Linear Models
Non-Life Insurance Pricing with Generalized Linear Models

Author: Esbjörn Ohlsson

Publisher: Springer Science & Business Media

Published: 2010-03-18

Total Pages: 181

ISBN-13: 3642107915

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Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration varoius properties of the insured object and the policy holder. Introduced by British actuaries generalized linear models (GLMs) have become today a the standard aproach for tariff analysis. The book focuses on methods based on GLMs that have been found useful in actuarial practice and provides a set of tools for a tariff analysis. Basic theory of GLMs in a tariff analysis setting is presented with useful extensions of standarde GLM theory that are not in common use. The book meets the European Core Syllabus for actuarial education and is written for actuarial students as well as practicing actuaries. To support reader real data of some complexity are provided at www.math.su.se/GLMbook.

Intelligent and Other Computational Techniques in Insurance
Intelligent and Other Computational Techniques in Insurance

Author: L. C. Jain

Publisher: World Scientific

Published: 2003

Total Pages: 692

ISBN-13: 9789812794246

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This book presents recent advances in the theory and implementation of intelligent and other computational techniques in the insurance industry. The paradigms covered encompass artificial neural networks and fuzzy systems, including clustering versions, optimization and resampling methods, algebraic and Bayesian models, decision trees and regression splines. Thus, the focus is not just on intelligent techniques, although these constitute a major component; the book also deals with other current computational paradigms that are likely to impact on the industry. The application areas include asset allocation, asset and liability management, cash-flow analysis, claim costs, classification, fraud detection, insolvency, investments, loss distributions, marketing, pricing and premiums, rate-making, retention, survival analysis, and underwriting. Contents: Insurance Applications of Neural Networks, Fuzzy Logic, and Genetic Algorithms; Practical Applications of Neural Networks in Property and Casualty Insurance; An Integrated Data Mining Approach to Premium Pricing for the Automobile Insurance Industry; Population Risk Management: Reducing Costs and Managing Risk in Health Insurance; Using Neural Networks to Predict in the Marketplace; Merging Soft Computing Technologies in Insurance-Related Applications; Robustness in Bayesian Models for BonusOCoMalus Systems; Using Data Mining for Modeling Insurance Risk and Comparison of Data Mining and Linear Modeling Approaches; System Intelligence and Active Stock Trading; The Algebra of Cash Flows: Theory and Application; and other papers. Readership: Graduate students, academics, researchers and practitioners involved with actuarial science, insurance, statistics and management science."

Statistics of Extremes
Statistics of Extremes

Author: Jan Beirlant

Publisher: John Wiley & Sons

Published: 2006-03-17

Total Pages: 522

ISBN-13: 0470012374

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Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.