Non-life Insurance Pricing With Generalized Linear Models
by Ohlsson, Esbjorn; Johansson, BjornEdition: 1st
Format: Paperback
Pub. Date: 2010-04-03
Publisher(s): Springer Verlag
Other versions by this Author
-
This Item Qualifies for Free Shipping!*
*Excludes marketplace orders.
List Price: $62.99
Rent Textbook
Select for Price
Rent Digital
$46.80
New Textbook
We're Sorry
Sold Out
Used Textbook
We're Sorry
Sold Out
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
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.
Table of Contents
| Non-Life Insurance Pricing | p. 1 |
| Rating Factors and Key Ratios | p. 2 |
| Basic Model Assumptions | p. 6 |
| Means and Variances | p. 8 |
| Multiplicative Models | p. 9 |
| The Method of Marginal Totals | p. 11 |
| One Factor at a Time? | p. 12 |
| Exercises | p. 13 |
| The Basics of Pricing with GLMs | p. 15 |
| Exponential Dispersion Models | p. 16 |
| Probability Distribution of the Claim Frequency | p. 18 |
| A Model for Claim Severity | p. 20 |
| Cumulant-Generating Function, Expectation and Variance | p. 21 |
| Tweedie Models | p. 24 |
| The Link Function | p. 26 |
| Canonical Link* | p. 29 |
| Parameter Estimation | p. 30 |
| The Multiplicative Poisson Model | p. 30 |
| General Result | p. 31 |
| Multiplicative Gamma Model for Claim Severity | p. 33 |
| Modeling the Pure Premium | p. 34 |
| Case Study: Motorcycle Insurance | p. 35 |
| Exercises | p. 37 |
| GLM Model Building | p. 39 |
| Hypothesis Testing and Estimation of ¿ | p. 39 |
| Pearson's Chi-Square and the Estimation of ¿ | p. 42 |
| Testing Hierarchical Models | p. 43 |
| Confidence Intervals Based on Fisher Information | p. 44 |
| Fisher Information | p. 44 |
| Confidence Intervals | p. 45 |
| Numerical Equation Solving* | p. 49 |
| Do the ML Equations Really Give a Maximum?* | p. 50 |
| Asymptotic Normality of the ML Estimators* | p. 51 |
| Residuals | p. 53 |
| Overdispersion | p. 54 |
| Estimation Without Distributional Assumptions | p. 58 |
| Estimating Equations | p. 58 |
| The Overdispersed Poisson Model | p. 60 |
| Denning Deviances from Variance Functions* | p. 60 |
| Miscellanea | p. 61 |
| Model Selection | p. 61 |
| Interaction | p. 62 |
| Offsets | p. 63 |
| Polynomial Regression | p. 63 |
| Large Claims | p. 63 |
| Deductibles* | p. 64 |
| Determining the Premium Level | p. 65 |
| Case Study: Model Selection in MC Insurance | p. 66 |
| Exercises | p. 66 |
| Multi-Level Factors and Credibility Theory | p. 71 |
| The Bühlmann-Straub Model | p. 74 |
| Estimation of Variance Parameters | p. 78 |
| Comparison with Other Notation* | p. 81 |
| Credibility Estimators in Multiplicative Models | p. 81 |
| Estimation of Variance Parameters | p. 84 |
| The Backfitting Algorithm | p. 84 |
| Application to Car Model Classification | p. 86 |
| More than One MLF | p. 87 |
| Exact Credibility* | p. 89 |
| Hierarchical Credibility Models | p. 90 |
| Estimation of Variance Parameters | p. 94 |
| Car Model Classification, the Hierarchical Case | p. 95 |
| Case Study: Bus Insurance | p. 96 |
| Exercises | p. 97 |
| Generalized Additive Models | p. 101 |
| Penalized Deviances | p. 102 |
| Cubic Splines | p. 104 |
| Estimation-One Rating Variable | p. 108 |
| Normal Case | p. 108 |
| Poisson Case | p. 110 |
| Gamma Case | p. 112 |
| Estimation-Several Rating Variables | p. 114 |
| Normal Case | p. 114 |
| Poisson Case | p. 117 |
| Gamma Case | p. 120 |
| Choosing the Smoothing Parameter | p. 121 |
| Interaction Between a Continuous and a Categorical Variable | p. 124 |
| Bivariate Splines | p. 125 |
| Thin Plate Splines | p. 126 |
| Estimation with Thin Plate Splines | p. 127 |
| Case Study: Trying GAMs in Motor Insurance | p. 132 |
| Exercises | p. 133 |
| Some Results from Probability and Statistics | p. 135 |
| The Gamma Function | p. 135 |
| Conditional Expectation | p. 135 |
| The Law of Total Probability | p. 136 |
| Bayes' Theorem | p. 137 |
| Unbiased Estimation of Weighted Variances | p. 138 |
| Some Results on Splines | p. 139 |
| Cubic Splines | p. 139 |
| B-splines | p. 145 |
| Thin Plate Splines | p. 152 |
| Some SAS Syntax | p. 165 |
| Parameter Estimation with Proc Genmod | p. 165 |
| Estimation of ¿ and Testing | p. 166 |
| SAS Syntax for Arbitrary Deviance* | p. 167 |
| Backfitting of MLFs | p. 168 |
| Fitting GAMs | p. 68 |
| Miscellanea | p. 168 |
| References | p. 171 |
| Index | p. 173 |
| Table of Contents provided by Ingram. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.