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## Book Description

A Hands-On Approach to Understanding and Using Actuarial Models

Computational Actuarial Science with R provides an introduction to the computational aspects of actuarial science. Using simple R code, the book helps you understand the algorithms involved in actuarial computations. It also covers more advanced topics, such as parallel computing and C/C++ embedded codes.

After an introduction to the R language, the book is divided into four parts. The first one addresses methodology and statistical modeling issues. The second part discusses the computational facets of life insurance, including life contingencies calculations and prospective life tables. Focusing on finance from an actuarial perspective, the next part presents techniques for modeling stock prices, nonlinear time series, yield curves, interest rates, and portfolio optimization. The last part explains how to use R to deal with computational issues of nonlife insurance.

Taking a do-it-yourself approach to understanding algorithms, this book demystifies the computational aspects of actuarial science. It shows that even complex computations can usually be done without too much trouble. Datasets used in the text are available in an R package (CASdatasets).

1. Preliminaries
2. Preface
3. Contributors
4. Chapter 1 Introduction
1. 1.1 R for Actuarial Science?
2. 1.2 Importing and Creating Various Objects, and Datasets in R
1. 1.2.1 Simple Objects in R and Workspace
2. 1.2.2 More Complex Objects in R: From Vectors to Lists
3. 1.2.3 Reading csv or txt Files
4. 1.2.4 Importing Excel&#174; Files and SAS&#174; Tables
5. 1.2.5 Characters, Factors and Dates with R
6. 1.2.6 Symbolic Expressions in R
3. 1.3 Basics of the R Language
1. 1.3.1 Core Functions
2. 1.3.2 From Control Flow to “Personal” Functions
3. 1.3.3 Playing with Functions (in a Life Insurance Context)
4. 1.3.4 Dealing with Errors
5. 1.3.5 Efficient Functions
6. 1.3.6 Numerical Integration
7. 1.3.7 Graphics with R: A Short Introduction
5. 1.5 Ending an R Session
6. 1.6 Exercises
5. Part I Methodology
6. Chapter 2 Standard Statistical Inference
1. 2.1 Probability Distributions in Actuarial Science
2. 2.2 Parametric Inference
4. 2.4 Linear Regression: Introducing Covariates in Statistical Infer­ence
5. 2.5 Aggregate Loss Distribution
6. 2.6 Copulas and Multivariate Distributions
7. 2.7 Exercises
7. Chapter 3 Bayesian Philosophy
1. 3.1 Introduction
2. 3.2 Bayesian Conjugates
3. 3.3 Computational Considerations
4. 3.4 Bayesian Regression
5. 3.5 Interpretation of Bayesianism
6. 3.6 Conclusion
7. 3.7 Exercises
8. Chapter 4 Statistical Learning
1. 4.1 Introduction and Motivation
2. 4.2 Logistic Regression
1. 4.2.1 Inference in the Logistic Model
2. 4.2.2 Logistic Regression on Categorical Variates
3. 4.2.3 Step-by-Step Variable Selection
4. 4.2.4 Leaps and Bounds
5. 4.2.5 Smoothing Continuous Covariates
6. 4.2.6 Nearest-Neighbor Method
3. 4.3 Penalized Logistic Regression: From Ridge to Lasso
4. 4.4 Classification and Regression Trees
5. 4.5 From Classification Trees to Random Forests
9. Chapter 5 Spatial Analysis
1. 5.1 Introduction
2. 5.2 Spatial Analysis and GIS
3. 5.3 Spatial Objects in R
1. 5.3.1 SpatialPoints Subclass
2. 5.3.2 SpatialPointsDataFrame Subclass
3. 5.3.3 SpatialPolygons Subclass
4. 5.3.4 SpatialPolygonsDataFrame Subclass
4. 5.4 Maps in R
5. 5.5 Reading Maps and Data in R
6. 5.6 Exploratory Spatial Data Analysis
1. 5.6.1 Mapping a Variable
2. 5.6.2 Selecting Colors
3. 5.6.3 Using the RgoogleMaps Package
4. 5.6.4 Generating KML Files
7. 5.7 Testing for Spatial Correlation
8. 5.8 Spatial Car Accident Insurance Analysis
9. 5.9 Spatial Car Accident Insurance Shared Analysis
10. 5.10 Conclusion
10. Chapter 6 Reinsurance and Extremal Events
1. 6.1 Introduction
2. 6.2 Univariate Extremes
3. 6.3 Inference
1. 6.3.1 Visualizing Tails
2. 6.3.2 Estimation
3. 6.3.3 Checking for the Asymptotic Regime Assumption
4. 6.3.4 Quantile Estimation
4. 6.4 Model Checking
5. 6.5 Reinsurance Pricing
11. Part II Life Insurance
12. Chapter 7 Life Contingencies
1. 7.1 Introduction
2. 7.2 Financial Mathematics Review
3. 7.3 Working with Life Tables
4. 7.4 Pricing Life Insurance
5. 7.5 Reserving Life Insurances
7. 7.7 Health Insurance and Markov Chains
8. 7.8 Exercises
13. Chapter 8 Prospective Life Tables
1. 8.1 Introduction
2. 8.2 Smoothing Mortality Data
3. 8.3 Lee—Carter and Related Forecasting Methods
4. 8.4 Other Mortality Forecasting Methods
5. 8.5 Coherent Mortality Forecasting
6. 8.6 Life Table Forecasting
7. 8.7 Life Insurance Products
8. 8.8 Exercises
14. Chapter 9 Prospective Mortality Tables and Portfolio Experience
1. 9.1 Introduction and Motivation
2. 9.2 Notation, Data, and Assumption
3. 9.3 The Methods
4. 9.4 Validation
5. 9.5 Operational Framework
15. Chapter 10 Survival Analysis
1. 10.1 Introduction
2. 10.2 Working with Incomplete Data
3. 10.3 Survival Distribution Estimation
4. 10.4 Regularization Techniques
5. 10.5 Modeling Heterogeneity
6. 10.6 Validation of a Survival Model
16. Part III Finance
17. Chapter 11 Stock Prices and Time Series
1. 11.1 Introduction
2. 11.2 Financial Time Series
3. 11.3 Heteroskedastic Models
4. 11.4 Application: Estimation of the VaR Based on the POT and GARCH Model
5. 11.5 Conclusion
18. Chapter 12 Yield Curves and Interest Rates Models
1. 12.1 A Brief Overview of the Yield Curve and Scenario Simulation
2. 12.2 Yield Curves
3. 12.3 Nelson—Siegel Model
4. 12.4 Svensson Model
19. Chapter 13 Portfolio Allocation
1. 13.1 Introduction
2. 13.2 Optimization Problems in R
3. 13.3 Data Sources
4. 13.4 Portfolio Returns and Cumulative Performance
5. 13.5 Portfolio Optimization in R
6. 13.6 Display Results
7. 13.7 Conclusion
20. Part IV Non-Life Insurance
21. Chapter 14 General Insurance Pricing
1. 14.1 Introduction and Motivation
2. 14.2 Claims Frequency and Log-Poisson Regression
3. 14.3 From Poisson to Quasi-Poisson
4. 14.4 More Advanced Models for Counts
5. 14.5 Individual Claims, Gamma, Log-Normal, and Other Regres­sions
6. 14.6 Large Claims and Ratemaking
7. 14.7 Modeling Compound Sum with Tweedie Regression
8. 14.8 Exercises
22. Chapter 15 Longitudinal Data and Experience Rating
1. 15.1 Motivation
2. 15.2 Linear Models for Longitudinal Data
3. 15.3 Generalized Linear Models for Longitudinal Data
1. 15.3.1 Specifying Generalized Linear Models with Random Effects
2. 15.3.2 Case Study: Experience Rating with Bonus—Malus Scales in R
23. Chapter 16 Claims Reserving and IBNR
1. 16.1 Introduction
2. 16.2 Development Triangles
3. 16.3 Deterministic Reserving Methods
4. 16.4 Stochastic Reserving Models
5. 16.5 Quantifying Reserve Risk
6. 16.6 Discussion
7. 16.7 Exercises
24. Chapter 17 Bibliography