R In Actuarial Pricing Teams
Chibisi Chima-Okereke
Mango Solutions
E-mail: cchima-okereke@mango-solutions.com
Agenda
Current software in actuarial analysis
What is R?
R as a functional language
Basic Examples
Actuarial pricing
GLM Example
Challenges and opportunities
Actuarial Survey
Geographical Area
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ( @Risk ): http://www.palisade.com/downloads/pdf/Pryor.pdf
Main Areas Of Work
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade 2006 ( @Risk ): http://www.palisade.com/downloads/pdf/Pryor.pdf
Main area of work in
which software is used
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ( @Risk ): http://www.palisade.com/downloads/pdf/Pryor.pdf
Percentage of respondents
using each package
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ( @Risk ): http://www.palisade.com/downloads/pdf/Pryor.pdf
Use of Statistical Packages
Percentage of statistical package
users using individual packages
UK Actuaries & CAS (Casualty Actuarial Society)
Source Palisade ( @Risk ): http://www.palisade.com/downloads/pdf/Pryor.pdf
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):
http://public.dhe.ibm.com/common/ssi/ecm/en/imw14297usen/IMW14297USEN.PDF
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?
What is R?
People
have
described
R as:
• A big calculator?
• A programming
language?
• A rapid prototyping tool?
• A free SAS?
• Statistical Analysis Tool?
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!
Current Actuarial R
Packages
actuar (loss distributions)
ChainLadder
lifecontingencies
LifeTables
http://cran.r-project.org/web/packages/
Functional Programming
Reference: http://nsaunders.wordpress.com/2010/08/20/a-brief-introductionto-apply-in-r/
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)
{plyr} Author: Hadley Wickham
http://www.jstatsoft.org/v40/i01/paper
I/O
Array
Data Frame
List
Discarded
Array
aaply
adply
alply
a_ply
Data Frame
daply
ddply
dlply
d_ply
List
laply
ldply
llply
l_ply
a*ply(.data, .margins, .fun, ...)
d*ply(.data, .variables, .fun, ...)
l*ply(.data, .fun, ...)
Example Data
Data Source (Simulated): Modern Actuarial Risk Theory Using R: Kaas, Goovaerts, Dhaene, and Denuit.
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)$coeff
theNames <- colnames(myCoeffs)
myCoeffs <- data.frame(myCoeffs)
myCoeffs <- data.frame(rownames(myCoeffs), myYear, myCoeffs)
colnames(myCoeffs) <- c("Coeff", "Year", theNames)
print(myYear)
return(myCoeffs[1,])
}
analysisOutPut <- lapply(2001:2010, doMyAnalysis)
analysisOutPut <- do.call(rbind, analysisOutPut)
rownames(analysisOutPut) <- 1:nrow(analysisOutPut)
Dynamics SQL Query Analysis
Combination Example
Coeff
Year
Estimate Std. Error z value
Pr(>|z|)
Intercept
2001
-0.76
0.03
-24.68
0.00
Intercept
2002
-0.77
0.03
-24.92
0.00
Intercept
2003
-0.80
0.03
-25.65
0.00
Intercept
2004
-0.78
0.03
-25.17
0.00
Intercept
2005
-0.80
0.03
-25.91
0.00
Intercept
2006
-0.76
0.03
-24.92
0.00
Intercept
2007
-0.70
0.03
-23.03
0.00
Intercept
2008
-0.76
0.03
-24.67
0.00
Intercept
2009
-0.79
0.03
-25.30
0.00
Intercept
2010
-0.75
0.03
-24.46
0.00
Plotting Analysis
myFun <- function(x){
hist(x$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
Plotting Analysis
GUI In R (claimsExploreR)
GUI In R (claimsExploreR)
Histogram of claim counts with BonusMalus and Age
Age : >65
Year : 2001
Age : >65
Year : 2002
Age : >65
Year : 2003
Age : >65
Year : 2004
Age : >65
Year : 2005
Age : >65
Year : 2006
Age : >65
Year : 2007
Age : >65
Year : 2008
Age : >65
Year : 2009
Age : >65
Year : 2010
Age : 18-23
Year : 2001
Age : 18-23
Year : 2002
Age : 18-23
Year : 2003
Age : 18-23
Year : 2004
Age : 18-23
Year : 2005
Age : 18-23
Year : 2006
Age : 18-23
Year : 2007
Age : 18-23
Year : 2008
Age : 18-23
Year : 2009
Age : 18-23
Year : 2010
Age : 24-64
Year : 2001
Age : 24-64
Year : 2002
Age : 24-64
Year : 2003
Age : 24-64
Year : 2004
Age : 24-64
Year : 2005
Age : 24-64
Year : 2006
Age : 24-64
Year : 2007
Age : 24-64
Year : 2008
Age : 24-64
Year : 2009
Age : 24-64
Year : 2010
40
30
20
10
0
Frequency
40
30
20
10
0
40
30
20
10
0
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
Exposure weighted claims count
BonusMalus
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
GUI In R (claimsExploreR)
Boxplots of exposure weighted severity with BonusMalus and Age
10
Exposure Weighted Severity (Log Scale)
10
10
10
10
10
10
10
Age : >65
Year : 2003
Age : >65
Year : 2004
Age : >65
Year : 2005
Age : >65
Year : 2006
Age : >65
Year : 2007
Age : >65
Year : 2008
Age : >65
Year : 2009
Age : >65
Year : 2010
Age : 18-23
Year : 2001
Age : 18-23
Year : 2002
Age : 18-23
Year : 2003
Age : 18-23
Year : 2004
Age : 18-23
Year : 2005
Age : 18-23
Year : 2006
Age : 18-23
Year : 2007
Age : 18-23
Year : 2008
Age : 18-23
Year : 2009
Age : 18-23
Year : 2010
Age : 24-64
Year : 2001
Age : 24-64
Year : 2002
Age : 24-64
Year : 2003
Age : 24-64
Year : 2004
Age : 24-64
Year : 2005
Age : 24-64
Year : 2006
Age : 24-64
Year : 2007
Age : 24-64
Year : 2008
Age : 24-64
Year : 2009
Age : 24-64
Year : 2010
3
2
1
4
3
2
1
4
10
3
10
Age : >65
Year : 2002
4
10
10
Age : >65
Year : 2001
2
1
BonusMalus
1
2
3
4
5
6
7
8
9
10
11
12
13
14
GLM Models in Pricing
Poisson – Frequency
Gamma – Severity
Negative Binomial for frequency {MASS}
Tweedie combines frequency and severity
{statmod}
Variable Selection
Criteria
What metrics
shall we use to
include/exclude
variables?
• Information Criteria
• AIC
• BIC (Multiple flavours)
• Significance of variable: ChiSquared/F-Test
• Consistency measures
• Other Measures
Automation Algoritms
What
mechanics will
we use to
select/exclude
variables?
•Forward Algorithm
•Backward
Algorithm
•Some other
bespoke method
Actuarial Pricing in R
Any statistical or data
analysis process can be
implemented in R but we
will think specifically
about GLMs
Example:
But actuarial pricing is
also the whole decision
making process around the
GLM ...
• glm(Claims ~ Location + CarType + Age +
..., data = myData, family = poisson(link
= “log”), offset = log(Exposure))
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
Automated Actuarial
Pricing
We need to defined the consolidation structure
for categorical variables e.g.
Location 1
Location 2
Location 3
Location 4
North
North
North
North
N.East
North
North
North
N.West
N.West
N.West
North
S.West
S.West
S.West
South
S.East
S.East
South
South
South
South
South
South
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
Example Process
Example Process
Example Process
Effects package
Effects plot of Age and Bonus Malus
Age : >65
Age : 24-64
Age : 18-23
150
Relativity (%)
140
130
120
110
1
2
3
4
5
6
7
8
9 10 11 12 13 14
1
2
3
4
5
6
7
8
9 10 11 12 13 14
Bonus Malus
effects package from John Fox: http://www.jstatsoft.org/v08/i15/paper
1
2
3
4
5
6
7
8
9 10 11 12 13 14
Example Process
Example Process:
Final Model
Final Charts
Final Model
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
Advantages of
R for GLM Analysis
R offers a
complete
statistical,
data
processing,
and analysis
environment
• 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
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