Case Study of How Actuaries Use R
Mark Chisholm
mark.chisholm@xlcatlin.com
R in Insurance 2015
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1
Agenda
• Background
• Multivariate modelling
• Interactive data visualisation
• Enriching data sets
• Lessons learned
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Background
The specialty insurance & reinsurance market offer protection for unique risks
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3
Multivariate Modelling
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Multivariate Modelling
• Many actuaries use MS Excel to evaluate multiple predictors using
one-way tables
Years on Claims Made
Row Labels
1 year
2 years
3 years
4 years
5 years
6 or more years
(blank)
Grand Total
Sum of Premium Sum of Incurred
950,000
1,083,000
250,000
187,500
1,800,000
1,651,500
1,450,000
1,290,500
2,300,000
2,128,500
4,600,000
4,449,500
11,350,000
10,790,500
Attachment Point USD
Row Labels
Sum of Premium Sum of Incurred
Less than 100k
1,150,000
932,500
At least 500k but less than 1m
8,200,000
7,971,500
Greater than 10m
2,000,000
1,886,500
(blank)
Grand Total
11,350,000
10,790,500
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LR
114.0%
75.0%
91.8%
89.0%
92.5%
96.7%
95.1%
LR
81.1%
97.2%
94.3%
95.1%
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Multivariate Modelling
• Obtaining an initial fit using multivariate modelling
techniques only requires a few lines of code
• Generalised linear models
• Techniques less widely used in insurance
• Discriminant analysis (MASS package)
• Random forests (randomForest package)
• Actuarial exams emphasise that one-way
techniques can mask exposure correlations
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Multivariate Modelling
• It is worth exploring different ideas
• Test different response variables and models
• Claim frequencies or severities
• Probability that there will be a claim notified
• Probability that the incurred loss ratio will exceed a benchmark
• Test different predictors
• Territory, premium band, revenues, deductible/excess, limit, etc.
• Experiment with including or not including different actuarial assumptions
such as trend, loss development, on-leveling, etc.
• Use external data to supplement your predictors (more on this later)
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Multivariate Modelling
• If you have already prepared your data in Excel, why not load it into R
and perform a multivariate analysis?
• You could:
• Save the table you wish to analyse as a tab-delimited text file
• Make use of packages such as as RExcel or XLConnect
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Multivariate Modelling
• An illustrative example of using logistic regression
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Multivariate Modelling
• An illustrative example of using logistic regression
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Interactive Data Visualisation
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Interactive Data Visualisation
• Information is often shared through standardised reports
• Hardcopy printout, pdf, MS Word doc, etc.
Line of Business 1
Territory
Country A
Country B
Country C
Premium
Number of Policies
Incurred Loss Claim Count
5,000,000
10
680,000
10,000,000
18
9,820,000
13,000,000
31
9,945,000
1
2
16
Incurred Loss Ratio
13.6%
98.2%
76.5%
Premium
Number of Policies
Incurred Loss Claim Count
9,000,000
82
10,300,000
13,000,000
101
12,450,000
4,000,000
52
4,105,000
58
82
44
Incurred Loss Ratio
114.4%
95.8%
102.6%
1
0
0
Incurred Loss Ratio
0.0%
0.0%
0.0%
Line of Business 2
Territory
Country A
Country B
Country C
Line of Business 3
Territory
Country A
Country B
Country C
Premium
Number of Policies
12,500,000
0
0
Incurred Loss
3
0
0
Claim Count
0
0
0
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Interactive Data Visualisation
• The shiny package lets you make interactive web sites very quickly
• Knowledge of JavaScript, HTML, and other web programming
languages is not required
• Supports the use of ggplot2, googleVis, etc. for graphics
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Interactive Data Visualisation
• Monthly loss development using shiny and googleVis
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Interactive Data Visualisation
• Drop-down lists
• Buttons
• Check boxes
• Radio buttons
• Free form entry
• Sliders
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Enriching Data Sets
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Enriching Data Sets
• Internal sources of data are often the first place to
look when trying to understand the characteristics
of policyholders
• Deductible/attachment point
• Territory
• Premium charged
• Perhaps various coding specific to the class of
business
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Enriching Data Sets
• External data sources should also be considered
• Underwriters may be able to point you to web sites with relevant data
• Demographic, geologic, economic, atmospheric, etc.
• Consider the raster package for working with geospatial data kept in
raster format (.bil files)
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Enriching Data Sets
• Working with raster images
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Lessons Learned
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Lessons Learned
• Common concerns
• “I’m not a programmer, I don’t have the time to
learn R”
• Focus on one bite-sized task to do in R and do
the rest using the tools you are comfortable
with
• Repeatable tasks
• Monthly MI with nice charts
• Fitting statistical models
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21
Lessons Learned
• Common concerns
• “I don’t have enough data to do multivariate analysis”
• If you have enough data to evaluate multiple variables on a oneway basis you have enough to try multivariate approaches
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Lessons Learned
• Common concerns
• “I downloaded R but it has a complex user interface and is difficult
to use”
• Use a search engine to find an “IDE for R” – this kind of tool makes
it much easier to write source code
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Lessons Learned
• A helpful resource for actuaries:
• Puts statistical ideas into
plain English, which is ideal
for practitioners
• Has labs with sample R
code, which makes it easy to
apply the techniques to your
company’s data sets
• Available for free from
author’s web site
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Questions?
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