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Computational Actuarial Science with R [Kõva köide]

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Edited by (University of Québec at Montreal, Canada)
  • Formaat: Hardback, 650 pages, kõrgus x laius: 254x178 mm, kaal: 1480 g, 22 Tables, black and white; 178 Illustrations, black and white
  • Sari: Chapman & Hall/CRC The R Series
  • Ilmumisaeg: 26-Aug-2014
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466592591
  • ISBN-13: 9781466592599
Teised raamatud teemal:
Computational Actuarial Science with RSuurem pilt
  • Formaat: Hardback, 650 pages, kõrgus x laius: 254x178 mm, kaal: 1480 g, 22 Tables, black and white; 178 Illustrations, black and white
  • Sari: Chapman & Hall/CRC The R Series
  • Ilmumisaeg: 26-Aug-2014
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466592591
  • ISBN-13: 9781466592599
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781466592599.html
Märksõnad:

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).

Arvustused

" the main objective of the book is that the reader gets interested in the topic and plays with the presented models and R codes in an active way. I have experienced that this goal can be easily reached for a large audience of readers because the presentation of the various arguments encourages an active learning of the concepts without being burdened by the theory." International Statistical Review, 83, 2015

" worthwhile reading and can be recommended to anyone who is interested in the computational aspects of actuarial science. The book contains many detailed worked examples, with R code fully integrated into the text. the book provides information and code that readers with any quantitative background can gain something from. It will naturally appeal to actuaries of all calibers, but it has a much wider audience of quantitative analysts using R for statistical modeling and data analysis in various fields. There are also good reasons to recommend this book to any science library." Journal of the Royal Statistical Society, Series A, 2015

Preface xvii
Contributors xxiii
List of Figures
xxv
List of Tables
xxxi
1 Introduction
1(72)
Arthur Charpentier
Rob Kaas
1.1 R for Actuarial Science?
2(9)
1.1.1 From Actuarial Science to Computational Actuarial Science
2(2)
1.1.2 The S Language and the R Environment
4(2)
1.1.3 Vectors and Matrices in Actuarial Computations
6(1)
1.1.4 R Packages
6(2)
1.1.5 S3 versus S4 Classes
8(3)
1.1.6 R Codes and Efficiency
11(1)
1.2 Importing and Creating Various Objects, and Datasets in R
11(23)
1.2.1 Simple Objects in R and Workspace
12(1)
1.2.2 More Complex Objects in R: From Vectors to Lists
13(1)
1.2.2.1 Vectors in R
13(4)
1.2.2.2 Matrices and Arrays
17(4)
1.2.2.3 Lists
21(1)
1.2.3 Reading csv or txt Files
22(4)
1.2.4 Importing Excel® Files and SAS® Tables
26(1)
1.2.5 Characters, Factors and Dates with R
27(1)
1.2.5.1 Strings and Characters
27(2)
1.2.5.2 Factors and Categorical Variables
29(2)
1.2.5.3 Dates in R
31(2)
1.2.6 Symbolic Expressions in R
33(1)
1.3 Basics of the R Language
34(28)
1.3.1 Core Functions
35(2)
1.3.2 From Control Flow to "Personal" Functions
37(1)
1.3.2.1 Control Flow: Looping, Repeating and Conditioning
37(1)
1.3.2.2 Writing Personal Functions
38(5)
1.3.3 Playing with Functions (in a Life Insurance Context)
43(1)
1.3.4 Dealing with Errors
44(1)
1.3.5 Efficient Functions
45(4)
1.3.6 Numerical Integration
49(3)
1.3.7 Graphics with R: A Short Introduction
52(1)
1.3.7.1 Basic Ready-Made Graphs
52(1)
1.3.7.2 A Simple Graph with Lines and Curves
53(2)
1.3.7.3 Graphs That Can Be Obtained from Standard Functions
55(2)
1.3.7.4 Adding Shaded Area to a Graph
57(1)
1.3.7.5 3D Graphs
58(1)
1.3.7.6 More Complex Graphs
59(3)
1.4 More Advanced R
62(6)
1.4.1 Memory Issues
62(1)
1.4.2 Parallel R
63(2)
1.4.3 Interfacing R and C/C++
65(3)
1.4.4 Integrating R in Excel®
68(1)
1.4.5 Going Further
68(1)
1.5 Ending an R Session
68(1)
1.6 Exercises
69(4)
I Methodology
73(214)
2 Standard Statistical Inference
75(52)
Christophe Dutang
2.1 Probability Distributions in Actuarial Science
76(13)
2.1.1 Continuous Distributions
76(6)
2.1.2 Discrete Distribution
82(2)
2.1.3 Mixed-Type Distributions
84(2)
2.1.4 S3 versus S4 Types for Distribution
86(3)
2.2 Parametric Inference
89(4)
2.2.1 Maximum Likelihood Estimation
90(1)
2.2.2 Moment Matching Estimation
91(1)
2.2.3 Quantile Matching Estimation
91(1)
2.2.4 Maximum Goodness-of-Fit Estimation
92(1)
2.3 Measures of Adequacy
93(6)
2.3.1 Histogram and Empirical Densities
93(1)
2.3.2 Distribution Function Plot
93(2)
2.3.3 QQ-Plot, PP-Plot
95(1)
2.3.4 Goodness-of-Fit Statistics and Tests
96(1)
2.3.5 Skewness--Kurtosis Graph
97(2)
2.4 Linear Regression: Introducing Covariates in Statistical Inference
99(4)
2.4.1 Using Covariates in the Statistical Framework
99(2)
2.4.2 Linear Regression Model
101(1)
2.4.3 Inference in a Linear Model
102(1)
2.5 Aggregate Loss Distribution
103(10)
2.5.1 Computation of the Aggregate Loss Distribution
104(3)
2.5.2 Poisson Process
107(3)
2.5.3 From Poisson Processes to Levy Processes
110(2)
2.5.4 Ruin Models
112(1)
2.6 Copulas and Multivariate Distributions
113(9)
2.6.1 Definition of Copulas
113(1)
2.6.2 Archimedean Copulas
114(1)
2.6.3 Elliptical Copulas
114(1)
2.6.4 Properties and Extreme Copulas
115(1)
2.6.5 Copula Fitting Methods
116(1)
2.6.6 Application and Copula Selection
117(5)
2.7 Exercises
122(5)
3 Bayesian Philosophy
127(38)
Benedict Escoto
Arthur Charpentier
3.1 Introduction
128(2)
3.1.1 A Formal Introduction
128(1)
3.1.2 Two Kinds of Probability
129(1)
3.1.3 Working with Subjective Probabilities in Real Life
129(1)
3.1.4 Bayesianism for Actuaries
130(1)
3.2 Bayesian Conjugates
130(11)
3.2.1 A Historical Perspective
131(1)
3.2.2 Motivation on Small Samples
132(4)
3.2.3 Black Swans and Bayesian Methodology
136(1)
3.2.4 Bayesian Models in Portfolio Management and Finance
137(1)
3.2.5 Relation to Buhlmann Credibility
138(2)
3.2.6 Noninformative Priors
140(1)
3.3 Computational Considerations
141(11)
3.3.1 Curse of Dimensionality
141(2)
3.3.2 Monte Carlo Integration
143(1)
3.3.3 Markov Chain Monte Carlo
144(2)
3.3.4 MCMC Example in R
146(3)
3.3.5 JAGS and Stan
149(3)
3.3.6 Computational Conclusion and Specific Packages
152(1)
3.4 Bayesian Regression
152(5)
3.4.1 Linear Model from a Bayesian Perspective
152(2)
3.4.2 Extension to Generalized Linear Models
154(2)
3.4.3 Extension for Hierarchical Structures
156(1)
3.5 Interpretation of Bayesianism
157(5)
3.5.1 Bayesianism and Decision Theory
159(1)
3.5.2 Context of Discovery versus Context of Justification
159(1)
3.5.3 Practical Classical versus Bayesian Statistics Revisited
160(2)
3.6 Conclusion
162(1)
3.7 Exercises
163(2)
4 Statistical Learning
165(42)
Arthur Charpentier
Stephane Tuffery
4.1 Introduction and Motivation
165(10)
4.1.1 The Dataset
166(2)
4.1.2 Description of the Data
168(1)
4.1.3 Scoring Tools
169(4)
4.1.4 Recoding the Variables
173(1)
4.1.5 Training and Testing Samples
174(1)
4.2 Logistic Regression
175(14)
4.2.1 Inference in the Logistic Model
175(3)
4.2.2 Logistic Regression on Categorical Variates
178(1)
4.2.3 Step-by-Step Variable Selection
179(1)
4.2.3.1 Forward Algorithm
180(1)
4.2.3.2 Backward Algorithm
181(2)
4.2.4 Leaps and Bounds
183(3)
4.2.5 Smoothing Continuous Covariates
186(2)
4.2.6 Nearest-Neighbor Method
188(1)
4.3 Penalized Logistic Regression: From Ridge to Lasso
189(4)
4.3.1 Ridge Model
190(1)
4.3.2 Lasso Regression
191(2)
4.4 Classification and Regression Trees
193(8)
4.4.1 Partitioning
193(3)
4.4.2 Criteria and Impurity
196(5)
4.5 From Classification Trees to Random Forests
201(6)
4.5.1 Bagging
202(1)
4.5.2 Boosting
203(1)
4.5.3 Random Forests
204(3)
5 Spatial Analysis
207(50)
Renato Assuncao
Marcelo Azevedo Costa
Marcos Oliveira Prates
Luis Gustavo Silva E Silva
5.1 Introduction
208(2)
5.1.1 Point Pattern Data
208(1)
5.1.2 Random Surface Data
208(1)
5.1.3 Spatial Interaction Data
209(1)
5.1.4 Areal Data
209(1)
5.1.5 Focus of This
Chapter
210(1)
5.2 Spatial Analysis and GIS
210(3)
5.3 Spatial Objects in R
213(10)
5.3.1 SpatialPoints Subclass
214(2)
5.3.2 SpatialPointsDataFrame Subclass
216(3)
5.3.3 SpatialPolygons Subclass
219(1)
5.3.3.1 First Elementary Example
219(2)
5.3.3.2 Second Example
221(2)
5.3.4 SpatialPolygonsDataFrame Subclass
223(1)
5.4 Maps in R
223(2)
5.5 Reading Maps and Data in R
225(3)
5.6 Exploratory Spatial Data Analysis
228(11)
5.6.1 Mapping a Variable
229(1)
5.6.2 Selecting Colors
230(1)
5.6.3 Using the RgoogleMaps Package
231(4)
5.6.4 Generating KML Files
235(1)
5.6.4.1 Adding a Legend to a KML File
236(3)
5.7 Testing for Spatial Correlation
239(4)
5.7.1 Neighborhood Matrix
239(2)
5.7.2 Other Neighborhood Options
241(1)
5.7.3 Moran's I Index
242(1)
5.8 Spatial Car Accident Insurance Analysis
243(7)
5.9 Spatial Car Accident Insurance Shared Analysis
250(5)
5.10 Conclusion
255(2)
6 Reinsurance and Extremal Events
257(30)
Eric Gilleland
Mathieu Ribatet
6.1 Introduction
257(1)
6.2 Univariate Extremes
258(5)
6.2.1 Block Maxima
259(1)
6.2.2 Exceedances above a Threshold
260(2)
6.2.3 Point Process
262(1)
6.3 Inference
263(15)
6.3.1 Visualizing Tails
264(1)
6.3.2 Estimation
265(1)
6.3.2.1 Generalized Extreme Value Distribution
265(2)
6.3.2.2 Poisson-Generalized Pareto Model
267(2)
6.3.2.3 Point Process
269(2)
6.3.2.4 Other Tail Index Estimates
271(1)
6.3.3 Checking for the Asymptotic Regime Assumption
272(1)
6.3.3.1 Mean Excess Plot
273(1)
6.3.3.2 Parameter Stability
274(1)
6.3.4 Quantile Estimation
275(3)
6.4 Model Checking
278(4)
6.4.1 Quantile Quantile Plot
278(1)
6.4.2 Probability-Probability Plot
279(1)
6.4.3 Return Level Plot
280(2)
6.5 Reinsurance Pricing
282(5)
6.5.1 Modeling Occurence and Frequency
283(1)
6.5.2 Modeling Individual Losses
284(3)
II Life Insurance
287(120)
7 Life Contingencies
289(30)
Giorgio Spedicato
7.1 Introduction
289(1)
7.2 Financial Mathematics Review
290(6)
7.3 Working with Life Tables
296(4)
7.4 Pricing Life Insurance
300(5)
7.5 Reserving Life Insurances
305(4)
7.6 More Advanced Topics
309(4)
7.7 Health Insurance and Markov Chains
313(4)
7.7.1 Markov Chain with R
313(2)
7.7.2 Valuation of Cash Flows
315(1)
7.7.3 APV of Benefits and Reserves
316(1)
7.8 Exercises
317(2)
7.8.1 Financial Mathematics
317(1)
7.8.2 Demography
317(1)
7.8.3 Pricing Life Insurance
317(1)
7.8.4 Reserving Life Insurances
318(1)
7.8.5 More Advanced Topics
318(1)
8 Prospective Life Tables
319(26)
Heather Booth
Rob J. Hyndman
Leonie Tickle
8.1 Introduction
319(1)
8.2 Smoothing Mortality Data
320(4)
8.2.1 Weighted Constrained Penalized Regression Splines
322(1)
8.2.2 Two-Dimensional P-Splines
322(2)
8.3 Lee--Carter and Related Forecasting Methods
324(11)
8.3.1 Lee--Carter (LC) Method
326(2)
8.3.2 Lee--Miller (LM) Method
328(1)
8.3.3 Booth--Maindonald--Smith (BMS) Method
329(2)
8.3.4 Hyndman--Ullah (HU) Method
331(3)
8.3.5 Robust Hyndman--Ullah (HUrob) Method
334(1)
8.3.6 Weighted Hyndman--Ullah (HUw) Method
335(1)
8.4 Other Mortality Forecasting Methods
335(2)
8.5 Coherent Mortality Forecasting
337(3)
8.6 Life Table Forecasting
340(1)
8.7 Life Insurance Products
341(2)
8.8 Exercises
343(2)
9 Prospective Mortality Tables and Portfolio Experience
345(38)
Julien Tomas
Frederic Planchet
9.1 Introduction and Motivation
346(1)
9.2 Notation, Data, and Assumption
347(2)
9.3 The Methods
349(9)
9.3.1 Method 1: Approach Involving One Parameter with the SMR
349(1)
9.3.2 Method 2: Approach Involving Two Parameters with a Semiparametric Relational Model
350(1)
9.3.3 Method 3: Poisson GLM Including Interactions with Age and Calendar Year
351(2)
9.3.4 Method 4: Nonparametric Smoothing and Application of the Improvement Rates
353(3)
9.3.5 Completion of the Tables: The Approach of Denuit and Goderniaux
356(2)
9.4 Validation
358(17)
9.4.1 First Level: Proximity between the Observations and the Model
358(10)
9.4.2 Second Level: Regularity of the Fit
368(2)
9.4.3 Third Level: Consistency and Plausibility of the Mortality Trends
370(5)
9.5 Operational Framework
375(8)
9.5.1 The Package ELT
376(1)
9.5.2 Computation of the Observed Statistics and Importation of the Reference
377(1)
9.5.3 Execution of the Methods
378(1)
9.5.4 Process of Validation
378(3)
9.5.5 Completion of the Tables
381(2)
10 Survival Analysis
383(24)
Frederic Planchet
Pierre-E. Therond
10.1 Introduction
383(2)
10.2 Working with Incomplete Data
385(6)
10.2.1 Data Importation and Some Statistics
386(1)
10.2.2 Building the Appropriate Database
387(1)
10.2.3 Some Descriptive Statistics
388(3)
10.3 Survival Distribution Estimation
391(3)
10.3.1 Hoem Estimator of the Conditional Rates
392(1)
10.3.2 Kaplan--Meier Estimator of the Survival Function
392(2)
10.4 Regularization Techniques
394(8)
10.4.1 Parametric Adjustment
396(2)
10.4.2 Semiparametric Adjustment: Brass Relational Model
398(1)
10.4.3 Nonparametric Techniques: Whittaker--Henderson Smoother
399(1)
10.4.3.1 Application
400(2)
10.5 Modeling Heterogeneity
402(3)
10.5.1 Semiparametric Framework: Cox Model
403(1)
10.5.2 Additive Models
404(1)
10.6 Validation of a Survival Model
405(2)
III Finance
407(66)
11 Stock Prices and Time Series
409(20)
Yohan Chalabi
Diethelm Wurtz
11.1 Introduction
409(1)
11.2 Financial Time Series
410(4)
11.2.1 Introduction
410(1)
11.2.2 Data Used in This
Chapter
411(1)
11.2.3 Stylized Facts
412(2)
11.3 Heteroskedastic Models
414(9)
11.3.1 Introduction
414(1)
11.3.2 Standard GARCH(1,1) Model
415(5)
11.3.3 Forecasting Heteroskedastic Model
420(1)
11.3.4 More Efficient Implementation
421(2)
11.4 Application: Estimation of the VaR Based on the POT and GARCH Model
423(4)
11.5 Conclusion
427(2)
12 Yield Curves and Interest Rates Models
429(18)
Sergio S. Guirreri
12.1 A Brief Overview of the Yield Curve and Scenario Simulation
429(3)
12.2 Yield Curves
432(4)
12.2.1 Description of the Datasets
432(2)
12.2.2 Principal Component Analysis
434(2)
12.3 Nelson-Siegel Model
436(8)
12.3.1 Estimating the Nelson--Siegel Model with R
440(4)
12.4 Svensson Model
444(3)
12.4.1 Estimating the Svensson Model with R
444(3)
13 Portfolio Allocation
447(26)
Yohan Chalabi
Diethelm Wurtz
13.1 Introduction
447(1)
13.2 Optimization Problems in R
448(4)
13.2.1 Introduction
448(1)
13.2.2 Linear Programming
449(1)
13.2.3 Quadratic Programming
450(1)
13.2.4 Nonlinear Programming
451(1)
13.3 Data Sources
452(3)
13.4 Portfolio Returns and Cumulative Performance
455(1)
13.5 Portfolio Optimization in R
456(11)
13.5.1 Introduction
456(2)
13.5.2 Mean--Variance Portfolio
458(2)
13.5.3 Robust Mean--Variance Portfolio
460(1)
13.5.4 Minimum Variance Portfolio
460(1)
13.5.5 Conditional Value-at-Risk Portfolio
461(5)
13.5.6 Minimum Drawdown Portfolio
466(1)
13.6 Display Results
467(3)
13.6.1 Efficient Frontier
467(1)
13.6.2 Weighted Return Plots
468(2)
13.7 Conclusion
470(3)
IV Non-Life Insurance
473(110)
14 General Insurance Pricing
475(36)
Jean-Philippe Boucher
Arthur Charpentier
14.1 Introduction and Motivation
476(2)
14.1.1 Collective Model in General Insurance
476(1)
14.1.2 Pure Premium in a Heterogenous Context
476(1)
14.1.3 Dataset
477(1)
14.1.4 Structure of the
Chapter and References
478(1)
14.2 Claims Frequency and Log-Poisson Regression
478(12)
14.2.1 Annualized Claims Frequency
478(2)
14.2.2 Poisson Regression
480(2)
14.2.3 Ratemaking with One Categorical Variable
482(2)
14.2.4 Contingency Tables and Minimal Bias Techniques
484(2)
14.2.5 Ratemaking with Continuous Variables
486(2)
14.2.6 A Poisson Regression to Model Yearly Claim Frequency
488(2)
14.3 From Poisson to Quasi-Poisson
490(2)
14.3.1 NB1 Variance Form: Negative Binomial Type I
490(1)
14.3.2 NB2 Variance Form: Negative Binomial Type II
491(1)
14.3.3 Unstructured Variance Form
492(1)
14.3.4 Nonparametric Variance Form
492(1)
14.4 More Advanced Models for Counts
492(7)
14.4.1 Negative Binomial Regression
493(2)
14.4.2 Zero-Inflated Models
495(2)
14.4.3 Hurdle Models
497(2)
14.5 Individual Claims, Gamma, Log-Normal, and Other Regressions
499(2)
14.5.1 Gamma Regression
499(1)
14.5.2 The Log-Normal Model
500(1)
14.5.3 Gamma versus Log-Normal Models
500(1)
14.5.4 Inverse Gaussian Model
501(1)
14.6 Large Claims and Ratemaking
501(6)
14.6.1 Model with Two Kinds of Claims
503(3)
14.6.2 More General Model
506(1)
14.7 Modeling Compound Sum with Tweedie Regression
507(3)
14.8 Exercises
510(1)
15 Longitudinal Data and Experience Rating
511(32)
Katrien Antonio
Peng Shi
Frank van Berkum
15.1 Motivation
511(2)
15.1.1 A Priori Rating for Cross-Sectional Data
511(1)
15.1.2 Experience Rating for Panel Data
512(1)
15.1.3 From Panel to Multilevel Data
513(1)
15.1.4 Structure of the
Chapter
513(1)
15.2 Linear Models for Longitudinal Data
513(19)
15.2.1 Data
513(4)
15.2.2 Fixed Effects Models
517(2)
15.2.3 Models with Serial Correlation
519(5)
15.2.4 Models with Random Effects
524(5)
15.2.5 Prediction
529(3)
15.3 Generalized Linear Models for Longitudinal Data
532(11)
15.3.1 Specifying Generalized Linear Models with Random Effects
532(3)
15.3.2 Case Study: Experience Rating with Bonus-Malus Scales in R
535(1)
15.3.2.1 Bonus-Malus Scales
535(1)
15.3.2.2 Transition Rules, Transition Probabilities and Stationary Distribution
536(3)
15.3.2.3 Relativities
539(4)
16 Claims Reserving and IBNR
543(40)
Markus Gesmann
16.1 Introduction
543(2)
16.1.1 Motivation
543(1)
16.1.2 Outline and Scope
544(1)
16.2 Development Triangles
545(3)
16.3 Deterministic Reserving Methods
548(4)
16.3.1 Chain-Ladder Algorithm
548(3)
16.3.2 Tail Factors
551(1)
16.4 Stochastic Reserving Models
552(25)
16.4.1 Chain-Ladder in the Context of Linear Regression
553(2)
16.4.2 Mack Model
555(4)
16.4.3 Poisson Regression Model for Incremental Claims
559(5)
16.4.4 Bootstrap Chain-Ladder
564(4)
16.4.5 Reserving Based on Log-Incremental Payments
568(9)
16.5 Quantifying Reserve Risk
577(2)
16.5.1 Ultimo Reserve Risk
577(1)
16.5.2 One-Year Reserve Risk
577(2)
16.6 Discussion
579(1)
16.7 Exercises
580(3)
Bibliography 583(22)
Index 605(8)
R Command Index 613
Arthur Charpentier is a professor of actuarial science at the University of Québec at Montréal. He is a fellow of the French Institute of Actuaries and holds a PhD in applied mathematics from K.U. Leuven. Dr. Charpentier is the co-author of two textbooks on mathematical models of nonlife insurance and has published several articles in peer-reviewed journals. He is also the editor of the blog freakonometrics.hypotheses.org