1. R In Actuarial Pricing Teams
Chibisi Chima-Okereke
Mango Solutions

2. Agenda Current software in actuarial analysis What is R?
R as a functional language
Basic Examples
Actuarial pricing
GLM Example
Challenges and opportunities

3. Actuarial Survey Geographical Area
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ):

4. Main Areas Of Work UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade 2006 ):

5. Main area of work in which software is used
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ):

6. Percentage of respondents using each package
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ):

7. Percentage of statistical package users using individual packages
Use of Statistical Packages
Percentage of statistical package users using individual packages
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ):

8. R is the programming language of statistics
Why should it not be the programming language of Actuaries?
Inadequate current incumbents
VBA: huge versioning issues and inadequate data manipulation and statistical function capabilities
Excel: Inappropriate for analysis
Proprietary Actuarial Software: No Granular Access To Processing Outputs
R offers so much in terms of data manipulation, statistical models
Spreadsheets are unstructured computer programs:
The Risks Of Using Spreadsheets for Statistical Analysis (IBM White Paper):

9. Excel Very labour intensive
Excel spreadsheets are unstructured computer programs
Problems with checking calculations and types of errors which can be silent and unknown
Do your spreadsheets start to grind to a halt with rather moderate sets of data?
Versioning excel files could be over 50MB each relative to script versions few KB. Imagine this across your network and the waste of space this encourages
Linking spreadsheets stability issues etc
VBA versioning problems, inadequate for data analysis and most useful purposes – harsh but true?

10. People have described R as:
What is R?
A big calculator?
A programming language?
A rapid prototyping tool?
A free SAS?
Statistical Analysis Tool?
People have described R as:

11. Useful R Features
Open source object oriented and functional programming language based on S+ designed for manipulating data/objects and carrying out statistical analysis
Easy connections to external programs databases, e.g. RODBC - very stable, dynamic SQL queries etc
Massive library of tools >>3400 packages
GUIs can be created in a straightforward way, gWidgets (GTK+, RGTK) package
Easy output formats, all picture files, data formats, even Excel!

12. Current Actuarial R Packages
actuar (loss distributions)
ChainLadder
lifecontingencies
LifeTables

13. Functional Programming
Reference:
apply(data, index, function)
lapply(list, function)
aggregate(data, by, FUN)
mapply(function(arg1, arg2), vector(arg1), vector(arg2), ...)
by(data, indices, function)
More “advanced/powerful” {plyr} package extends the apply functionality (Hadley Wickham)

14. {plyr} Author: Hadley Wickham
I/O
Array
Data Frame
List
Discarded
aaply
adply
alply
a_ply
daply
ddply
dlply
d_ply
laply
ldply
llply
l_ply
a*ply(.data, .margins, .fun, ...)
d*ply(.data, .variables, .fun, ...)
l*ply(.data, .fun, ...)

15. Example Data
Data Source (Simulated): Modern Actuarial Risk Theory Using R: Kaas, Goovaerts, Dhaene, and Denuit.

16. Dynamic SQL Query Example
require(RODBC)
doMyAnalysis <- function(myYear = 2001){
sqlString <- paste("SELECT * FROM policyClaims WHERE Year='",myYear,"'", sep = "")
myData <- sqlQuery(channel = odbcConnect(dsn = "InsuranceData"), query = sqlString)
odbcCloseAll()
myGlm <- glm(noclaims ~ age + bonusmalus + region + mileage, data = myData, offset = log(exposure), family = poisson(link = "log"))
myCoeffs <- summary(myGlm)$coeff
theNames <- colnames(myCoeffs)
myCoeffs <- data.frame(myCoeffs)
myCoeffs <- data.frame(rownames(myCoeffs), myYear, myCoeffs)
colnames(myCoeffs) <- c("Coeff", "Year", theNames)
print(myYear)
return(myCoeffs[1,]) }
analysisOutPut <- lapply(2001:2010, doMyAnalysis)
analysisOutPut <- do.call(rbind, analysisOutPut)
rownames(analysisOutPut) <- 1:nrow(analysisOutPut)

17. Dynamics SQL Query Analysis Combination Example
Coeff
Year
Estimate
Std. Error
z value
Pr(>|z|)
Intercept
2001
-0.76
0.03
-24.68
0.00
2002
-0.77
-24.92
2003
-0.80
-25.65
2004
-0.78
-25.17
2005
-25.91
2006
2007
-0.70
-23.03
2008
-24.67
2009
-0.79
-25.30
2010
-0.75
-24.46

18. Plotting Analysis myFun <- function(x){
hist(x$GrossIncurred, col = "blue", xlab = "GIC", main = paste("Histogram of GIC for bonus malus \n group ", x$BonusMalus[1], " and year ", x$Year[1], sep = "")) }
pdf(file = paste(myFolder, "myPlots.pdf", sep = ""), width = 7, height = 7)
by(policyTable, list("Year" = policyTable$Year, "BonusMalus" = policyTable$BonusMalus), FUN = myFun)
dev.off()
C:\Users\cchima-okereke\Documents\R\RScripts\ActuarialPricing\tmp\myPlots.pdf

19. Plotting Analysis

20. GUI In R (claimsExploreR)

21. GUI In R (claimsExploreR)

22. GUI In R (claimsExploreR)

23. Pricing GLM Software
Very limited choice of off the shelf pricing tools basically one: EMBLEM (Towers Watson)
Current tools do not allow enough access to underlying functionality and tend to be very labour intensive
Other statistical software e.g. SAS are extremely expensive to extend across organisations or do not have the range of statistical functionality required

24. Actuarial Pricing Teams
4-7 Actuarial Analysts+ Manager + Off The Shelf Solutions => Inefficiencies + Repetitive Tasks
Typical Team
2-4 Actuarial Analysts + Manager + R => Efficient Automated System + Creative Analysis
Team Using R +

25. GLM Models in Pricing Poisson – Frequency Gamma – Severity
Negative Binomial for frequency {MASS}
Tweedie combines frequency and severity {statmod}

26. Variable Selection Criteria
Information Criteria
AIC
BIC (Multiple flavours)
Significance of variable: Chi-Squared/F-Test
Consistency measures
Other Measures
What metrics shall we use to include/exclude variables?

27. What mechanics will we use to select/exclude variables?
Automation Algoritms
Forward Algorithm
Backward Algorithm
Some other bespoke method
What mechanics will we use to select/exclude variables?

28. Actuarial Pricing in R
Any statistical or data analysis process can be implemented in R but we will think specifically about GLMs
glm(Claims ~ Location + CarType + Age + ..., data = myData, family = poisson(link = “log”), offset = log(Exposure))
Example:
But actuarial pricing is also the whole decision making process around the GLM ...

29. Automated pricing Process Structure in R
Claim Counts analysis
Load data from database
Carry out pre-specified step algorithm with variable aggregation
Variable selection criteria
Check variable consistency
Decide to reject/accept variable
Severity analysis
Obtain Final Models
Continuously writing desired outputs, PDF, log files, documentation, model plots, coefficients etc

30. Automated Actuarial Pricing
We need to defined the consolidation structure for categorical variables e.g.
Location 1
Location 2
Location 3
Location 4
North
N.East
N.West
S.West
South
S.East

31. Outputting Results
R has perhaps the most extensive choices for outputs of analysis
Link to Excel
Text files, e.g. CSV etc
Charting Output: picture files: jpeg, tiff, png, pdf, etc..
Report generation: PDF(Sweave - Latex), Word
PowerPoint direct output
Printing log reports of process

32. Example Process

33. Example Process

34. Example Process

35. Effects package
effects package from John Fox:

36. Example Process

37. Example Process: Final Model

38. Final Charts

39. Final Model

40. Potential Scheme for analytical process
Data residing in some database
Connect to R, RODBC, RPostgreSQL, RODM etc.
Carry out analysis in R
Write results to PDF, any picture format, push to Latex, Excel, CSV, etc

41. My R Actuarial Experiences
GLM for risk ranking of policies
Geo-Mapping applications & reporting
Ad-hoc simple Bayesian Analysis of claims probability based on previous experiences
Extreme value analysis to obtain large claims thresholds for various classes
Location based risk analysis
General reporting tool
But there is so much more potential! I was barely scratching the surface
R is much more stable that common analytical tools e.g. Database connections and other functionality

42. Advantages of R for GLM Analysis
Standard actuarial GLM techniques are available, e.g. splines, interaction terms etc.
The best plotting functions of any statistical package
More advanced techniques are available, GAM, GMM, GNM, GHMM, MCMC methods – too many packages to list here!
Bespoke methods and new actuarial techniques can be readily implemented in R while they are unavailable in standard actuarial software
Easy to integrate and fully customisable in any analytical environment
Complete array of statistical/analysis tools, clustering, neural nets, GRM, tree models, bootstrapping, Bayesian techniques, ODE/PDE, HMMs, contingency tables, survival analysis, copulas, extreme value analysis, geospatial analysis and visualisation
R offers a complete statistical, data processing, and analysis environment

43. Challenges & Opportunities
If you are new to R, do something small to begin with test R out
IT support for R
There is great need for training and generation of material to enable actuarial analysts to use R
For mere mortals (like me) the learning curve is tough and the documentation appears ambiguous
R & Hadoop and R & Oracle
See me later for live R demos