mages' blog

Claims Inflation - a known unknown

2013-05-14T07:20:00.000+01:00

Over the last year I worked with two colleagues of mine on the subject of inflation and claims inflation in particular. I didn't expect it to be such a challenging topic, but we ended up with more questions than answers. The key question and biggest challenge is to define what inflation, or indeed claims inflation actually is and how to measure it. We published a summary of our thoughts and findings in this month's issue of The Actuary.

Last year's discussion about the differences between the retail price index (RPI) and consumer price index (CPI) in the UK only exemplified the challenge. The economist Tim Harford illustrated the differences between the RPI and CPI with a simple example of price changes for a shirt and blouse in his Radio 4 programme More or Less. The radio podcast is still available from the BBC. Start listening after about 18 minutes into the show.

R in Insurance: Programme and Abstracts published

2013-05-07T17:17:00.000+01:00

I am delighted to announce that the programme and abstracts for the first R in Insurance conference at Cass Business School in London, 15 July 2013, have been published.

The conference committee received strong abstracts from academia and the industry, covering:

Pricing
Reserving
Data mining
Capital modelling
Automate reporting
Catastrophe modelling
High-performance computing
Software development management

Register by the end of May to get the early bird booking fee.

We gratefully acknowledge the sponsorship of Mango Solutions and CYBAEA, without whom the event wouldn't be possible.

Programme and Abstracts

How to change the alpha value of colours in R

2013-04-30T07:08:00.000+01:00

Often I like to reduce the alpha value (level of transparency) of colours to identify patterns of over-plotting when displaying lots of data points with R. So, here is a tiny function that allows me to add an alpha value to a given vector of colours, e.g. a RColorBrewer palette, using col2rgb and rgb, which has an argument for alpha, in combination with the wonderful apply and sapply functions.

The example below illustrates how this function can be used with colours provided in different formats, thanks to the col2rgb function.

Review: Kölner R Meeting 12 April 2013

2013-04-23T07:34:00.000+01:00

Our 5th Cologne R user group meeting was the best attended meeting so far, with 20 members finding their way to the Institute of Sociology for two talks by Diego de Castillo on shiny and Stephan Holtmeier on cluster analysis, followed by beer and schnitzel at the Lux, a gastropub nearby.

Shiny

Diego gave an overview of the design principles behind shiny, which provides a powerful API to build web apps in pure R. His explanation of the reactive programming model was particularly helpful to understand how shiny works under the hood and why it is so responsive. His live demonstrations of shiny even included shiny server, which he had running in a virtual machine. Diego's slides are available via our Meetup site.

Diego de Castillo: Introduction to shiny

You can hear more from Diego and me at the UseR!2013 conference in Albacete, where we will give a googleVis tutorial. We will touch on googleVis on shiny as well. A dedicated shiny tutorial will be given in the afternoon by Josh and Winston from RStudio.

Cluster analysis

Stephan Holtmeier, who is a psychologist by background, presented an introduction to cluster analysis with R, motivated by his work in analysing survey data. As a toy example he used a 360° feedback survey of a group of managers within a big company. In his example he wanted to understand the profile of those managers better. Stephan illustrated how a cluster analysis can help to identify groups of managers with similar strengths, e.g. for communication, leadership and/or performance. Depending on how he measured the distance between managers he could look for people who have similar levels of competency or a similar profile (correlation). Stephan also touched on the differences between hierarchical and centroid based cluster analysis, such as k-means. You can find Stephan's slides (in German) also on our Meetup site.

Stephan Holtmeier: Cluster Analysis with R

For more information on cluster analysis functions in R see also the cluster task view on CRAN. If you would like to get an overview of how psychologists look at data, then check out William Revelle's vignette of the psych package. Finally, if you are interested in how a k-means cluster analysis can be used for image manipulation, see an earlier post of mine.

Next Kölner R meeting, 19 July 2013

The next meeting has been scheduled for 19 July. Günter Faes will present his experiences using the XLConnect package as an interface between R and Excel. Dietmar Janetzko agreed to present how he used R and Twitter to predict exchange rate movements. Of course, the evening will close with a few Kölsch in a nearby beer-garden.

Please get in touch if you would like to present and share your experience, or indeed if you have a request for a topic you would like to hear more about. For more details see also our Meetup page.

Thanks again to Bernd Weiß for hosting the event and Revolution Analytics for their sponsorship.

Test Driven Analysis?

2013-04-16T07:52:00.000+01:00

At the last LondonR meeting Francine Bennett from Mastodon C shared some of her experience and findings from an analysis of a large prescriptions data set of the UK's national health service (NHS). However, it was her last slide, which I found the most thought provoking. It asked for the definition of the following term:

Test-driven analysis?

Francine explained that test driven development (TDD) is a concept often used in software development for quality assurance and she wondered if a similar approach could be also used for data analysis. Unfortunately the audience couldn't provide her with the answer, but many expressed that they face similar challenges. So do I.

Indeed, how do I go about test driven analysis? How do I know that I haven't made a mistake, when I start an analysis of a new data set? Well, I don't. But I try to mitigate risks. Similar to TDD, I consider which outputs I should expect from my analysis. Those outputs form the test scenarios of my analysis. Basically I try to write down everything I know, before I start working with the data, e.g.

any other data sets or reports I can use for cross referencing,
any back-of-the-envelope analysis I can carry out to provide ballpark answers,
any relativities and ratios which should hold true,
any known boundaries and thresholds,
test scenarios for my code with small well known data, for which I know the outcome,
names of experts, who could sense check and peer review my output.

But most importantly: I try to think long and hard which questions I want to answer, following the advice of John Tukey: Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.

How to set axis options in googleVis

2013-04-09T07:57:00.000+01:00

Setting axis options in googleVis charts can be a bit tricky. Here I present two examples where I set several options to customise the layout of a line and combo chart with two axes.

The parameters have to be set in line with the Google Chart Tools API, which uses a JavaScript syntax. In googleVis chart options are set via a list in the options argument. Some of the list items can be a bit more complex, often wrapped in {} brackets, e.g. for various formatting options or in [] brackets, if there are multiple series to consider. Within those brackets sub-options are set via argument : value, using the : character for assignments.

There are many other options as part of the Google Chart Tools API, which are not supported by googleVis yet, such as columns roles, controls and dashboards, etc. Please get in touch if you have ideas in this regard and/or would like to collaborate.

In my first example I display two series of dummy data in a line chart with two axes. The left hand scale is in percentages and the right hand scale in amounts. Note in the code below how I set the various parameters and the placements of the different kinds of brackets.
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Next Kölner R User Meeting: 12 April 2013

2013-04-08T07:00:00.001+01:00

Quick reminder: The next Cologne R user group meeting is scheduled for this Friday, 12 April 2013. We will discuss cluster analysis and shiny. Further details and the agenda are available on our KölnRUG Meetup site. Please sign up if you would like to come along. Notes from the last Cologne R user group meeting are available here.

Thanks also to Revolution Analytics, who sponsors the Cologne R user group as part of their vector programme.

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Top 10 tips to get started with R

2013-04-02T08:10:00.000+01:00

Be motivated. R has a steep learning curve. Find a problem you can't solve otherwise. E.g. plotting multivariate data, a statistical analysis for which an R function exists already.
Download and install R. Get to know the R console. Learn how to install additional packages, how to access the history, how to use auto completion and open the help system. Review the R Installation and Administration manual and check out the free books section on CRAN.
Get familiar with the R help files. They can appear cryptic at the start, but there is a structure to them. Read and re-read a couple of help files again and again. Look out for the input and output sections, execute the examples, run the demos, e.g. demo(graphics). Subscribe to R-help and read questions and answers, check out stackoverflow, follow blogs. Search with Rseek.org.
Learn how to get your data into R. The easiest way is usually via a CSV-file (CSV=comma separated values), using read.csv. Look into XLConnect, if you have to deal with spreadsheet files. Move on to write queries against data bases, e.g. using RODBC. Skim through the R Data Import/Export manual.
Try to understand the different data types in R and how to modify them. What are the differences between a matrix and a data frame? What is a factor? What is a list? Think about the different use cases. Review the Introduction to R manual.
Do charts! Lots of charts. They are rewarding and keep you motivated. Be inspired by the R Graph Gallery. Check out the following packages: lattice, plotrix, ggplot2, deducer, googleVis.
Learn how you can modify and reshape data in R and apply functions on subsets using by, apply, lapply, ave, reshape, sweep, with, within, etc. Set aside a weekend to think about these functions.
Write your R code into files instead of typing it all into the R console. Use an integrated development environment (IDE), e.g. ESS Emacs, RStudio, StatET Eclipse.
Understand the concept of functions. Write a function, which gives "Hello World" back. Modify it, so it has an input argument NAME and it prints "Hello NAME". Review the code of existing R functions. Copy from existing code.
Document your code! Start your code by explaining what you want to achieve and only code that much, then write down the next step in plain English and code again. How will you know that your code does what you want it to do? Testing can help. Think about your code style and how you will be versioning your files.

Bonus tip

Be patient. Going mad? Check out the R Inferno by Pat Burns.

ChainLadder 0.1.5-6 released on CRAN

2013-03-26T07:16:00.001Z

Last week we released version 0.1.5-6 of the ChainLadder package on CRAN. The ChainLadder package provides statistical models, which are typically used for the estimation of outstanding claims reserves in general insurance. The package vignette gives an overview of the package functionality.

Output of plot(MackChainLadder(GenIns))

Since the last CRAN release Dan Murphy added new features to the MackChainLadder function and we fixed a bug in BootChainLadder. Here are he details:

New Features

The list output of the MackChainLadder function now includes the parameter risk and process risk breakdowns of the total risk estimate for the sum of projected losses across all origin years by development age.
The Mack Method's recursive parameter risk calculation now enables Mack's original two-term formula (the default) and optionally the three-term formula found in Murphy's 1994 paper and in the 2006 paper by Buchwalder, Bühlmann, Merz, and Wüthrich.
A few more Mack Method examples.

Bug Fixes

The phi-scaling factor in BootChainLadder was incorrect. Instead of calculating the number of data items in the upper left triangle as n*(n+1)/2, n*(n-1)/2 was used. Thanks to Thomas Girodot for reporting this bug.

Please get in touch if you would like to collaborate or find any issues or bugs.

Join me at the first R in Insurance conference at Cass Business School in London, 15 July 2013.

Submit a talk for the first R in Insurance conference

2013-03-25T07:40:00.000Z

The registration for the first R in Insurance is open and there is still time to submit a talk / lightning talk.

The conference will take place at Cass Business School in London on Monday, 15 July 2013. This is the Monday following the useR! 2013 conference in Spain. Thus, if you come from overseas to Spain, why not stop in London on your way back?

All further information and registration details are available on the Cass Business School conference site.

googleVis 0.4.2 with support for shiny released on CRAN

2013-03-19T07:40:00.000Z

The new version of googleVis 0.4.2 is now available via CRAN. Many thanks to all who provided feedback on version 0.4.0 and particularly to Sebastian Campbell, John Maindonald and Aonan Zhang. As usual, if you find any issues or bugs, please send us an email or add a line to our online issues log.

With version 0.4.0 we introduced support for googleVis on shiny. See my previous post for more details and examples.

The CRAN release of googleVis 0.4.2 has some further improvements:

New shiny and FAQ sections in package vignette
Core charts (e.g. line, area, scatter, bar, column and combo charts) accept now also date variables for the x-axis
Typos in the Stock and Andrew data sets have been fixed
The WorldBank demo uses now the WDI package to download data from the World Bank, see the R code below

Loading
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How to use optim in R

2013-03-12T07:49:00.000Z

A friend of mine asked me the other day how she could use the function optim in R to fit data. Of course there are functions for fitting data in R and I wrote about this earlier. However, she wanted to understand how to do this from scratch using optim.

The function optim provides algorithms for general purpose optimisations and the documentation is perfectly reasonable, but I remember that it took me a little while to get my head around how to pass data and parameters to optim. Thus, here are two simple examples.

I start with a linear regression by minimising the residual sum of square and discuss how to carry out a maximum likelihood estimation in the second example.

Minimise residual sum of squares

I start with an x-y data set, which I believe has a linear relationship and therefore I'd like to fit y against x by minimising the residual sum of squares.

dat=data.frame(x=c(1,2,3,4,5,6), 
               y=c(1,3,5,6,8,12))

Next, I create a function that calculates the residual sum of square of my data against a linear model with two parameter. Think of y = par[1] + par[2] * x.

min.RSS <- function(data, par) {
              with(data, sum((par[1] + par[2] * x - y)^2))
             }

Optim minimises a function by varying its parameters. The first argument of optim are the parameters I'd like to vary, par in this case; the second argument is the function to be minimised, min.RSS. The tricky bit is to understand how to apply optim to your data. The solution is the ... argument in optim, which allows me to pass other arguments through to min.RSS, here my data. Therefore I can use the following statement:

result <- optim(par = c(0, 1), min.RSS, data = dat)
# I find the optimised parameters in result$par
# the minimised RSS is stored in result$value
result
## $par
## [1] -1.267  2.029
## 
## $value
## [1] 2.819
## 
## $counts
## function gradient 
##       89       NA 
## 
## $convergence
## [1] 0
## 
## $message
## NULL

Let me plot the result:

plot(y ~ x, data = dat)
abline(a = result$par[1], b = result$par[2], col = "red")

Create an R package from a single R file with roxyPackage

2013-03-05T07:00:00.000Z

Documenting code can be a bit of a pain. Yet, the older (and wiser?) I get, the more I realise how important it is. When I was younger I said 'documentation is for people without talent'. Well, I am clearly loosing my talent, as I sometimes struggle to understand what I programmed years ago. Thus, anything that soothes the pain of writing and maintaining documentation must be good and should help me to better understand my 'old me' in the future.

Ideally I want my R code and documentation in as few files as possible. A good start to achieve this is using roxygen2, an R package which has been around for some time. It allows me to tie R code together with the documentation in the same file and helps considerably in maintaining R packages.

The roxyPackage by Meik Michalke goes a step further, building on roxygen2. Meik presented his package at the Cologne R user group meeting a few weeks ago and I was intrigued by it. As I said in my notes to the meeting, with roxyPackage I can create a package from a single file of R code and documentation.

Here is an example of one R file to build a package using roxyPackage. For my toy example I wrote a doughnut plot function in R, something which is clearly missing ;)

I took the basic pie chart function and amended it to plot another white disc in the middle. On top of the function code I wrote the help file documentation using the roxygen2 syntax.
Read more »

First steps of using googleVis on shiny

2013-02-26T06:47:00.000Z

The guys at RStudio have done a fantastic job with shiny. It is really easy to build web apps with R using shiny. With the help of Joe Cheng from RStudio we figured out a way to make googleVis work on shiny as well. This allows you to make use of the Google Charts Tools in your shiny app directly from R. What I present here are three initial examples which seem to work in most browsers. The third example even uses a neat trick to create an animated geo chart.

However, before we upload the next version of googleVis to CRAN we decided to present a preview of version 0.4.0 here, asking for feedback. It would not be fair on the guys behind CRAN to release something into the wild, only to be told by users within a few days that we missed something. Hence, you can get the new version of googleVis only from the download page of our project site for the time being.

You may have read the post on RStudio's blog that the shiny API changed slightly: the reactivePlot and reactiveText functions have been renamed to renderPlot and renderText with simplified input parameters. Thanks to Joe, there is now also a renderGvis function as part of the googleVis package, which works in very much the same way as the other two.

To run the following examples you need shiny version 0.4.0 and googleVis version 0.4.0 or higher. Note that the charts below are not screen shots, but real apps hosted on RStudio's infrastructure.
Read more »

Registration for 'R in Insurance' conference has opened

2013-02-19T19:30:00.000Z

The registration for the first conference on R in Insurance on Monday 15 July 2013 at Cass Business School in London has opened.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

The 2013 R in Insurance conference builds upon the success of the R in Finance and R/Rmetrics events. We expect invited keynote lectures by:

Professor Alexander McNeil, Department of Actuarial Science & Statistics
Heriot-Watt University: Implementing CreditRisk+ in R with the Faster Fourier Transform
Trevor Maynard, Head of Exposure Management and Reinsurance, Lloyd's: There is an R in Lloyd's

We invite you to submit a one-page abstract for consideration. Both academic and practitioner proposals related to R are encouraged.

The submission deadline for abstracts is 28 March 2013. Please email your abstract (in txt or pdf format) to rinsuranceconference at gmail dot com.

The conference committee consists of:

Details about the registration and abstract submission are given on the new dedicated R in Insurance page at Cass Business School.

The organisers, Andreas Tsanakas and Markus Gesmann, gratefully acknowledge the sponsorship of Mango Solutions.

New Data Scientist role at Lloyd's

2013-02-15T13:47:00.000Z

Lloyd's of London is looking for a Data Scientist as part of the Analysis team. See Lloyd's career web site for more details.

Review: Kölner R Meeting 6 February 2013

2013-02-12T17:49:00.000Z

The fourth Cologne R user meeting took place last Wednesday at the Institute of Sociology. Thanks to Bernd Weiß for hosting the event and Revolution Analytics for their sponsorship.

We had two fantastic talks by Klaus Jacobi and M.eik Michalke. Klaus talked about Eliminating cloud pixels in satellite images via chronological interpolation and Meik presented his new roxyPackage package, which makes it even easier to maintain R packages with roxygen2.

Eliminating cloud pixels in satellite images via chronological interpolation

Klaus gave a great case study about his consulting work as a water engineer in Asia, where he used R to analyse the snow melting process in the mountains of Pakistan.

Images of snow melting over time. Klaus Jacobi

About half of the fresh water in some regions of Pakistan is sourced from snow meting during the spring season. The water is captured in dams and as the snow only melts slowly the water supply is much more predictable than the water from the monsoon season, which is the other key source of fresh water during the year.
Read more »

Next Kölner R User Meeting: 6 February 2013

2013-02-05T07:08:00.000Z

Quick reminder: The next Cologne R user group meeting is scheduled for tomorrow, 6 February 2013. All details and the agenda are available on the KölnRUG Meetup site. Please sign up if you would like to come along. Notes from the last Cologne R user group meeting are available here.

Thanks also to Revolution Analytics, who are sponsoring the Cologne R user group as part of their vector programme.

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Follow the ants to richness

2013-01-29T08:10:00.000Z

A friend of mine told me the secret of making money at the stock market. "It's easy", he said.

All I would have to do is to buy a big jar of ants. Then I should observe the ants movement on my kitchen table, while following the stock market.

I shall keep the ants which walk in line with the stock market and remove those who don't. Eventually I would have one ant left that walked all the way in line with the stock market.

Bingo! This is the one I have to keep feeding well and observe, as it clearly can predict the movements of the stock market.

For more complex problems I recommend to use animals with bigger brains.

Reserving based on log-incremental payments in R, part III

2013-01-22T23:18:00.000Z

This is the third post about Christofides' paper on Regression models based on log-incremental payments [1]. The first post covered the fundamentals of Christofides' reserving model in sections A - F, the second focused on a more realistic example and model reduction of sections G - K. Today's post will wrap up the paper with sections L - M and discuss data normalisation and claims inflation.

I will use the same triangle of incremental claims data as introduced in my previous post. The final model had three parameters for origin periods and two parameters for development periods. It is possible to reduce the model further as Christofides illustrates in section L onwards by using an inflation index to bring all claims payments to current value and a claims volume adjustment or weight for each origin period to normalise the triangle.

In his example Christofides uses claims volume adjustments for the origin years and an earning or inflation index for the different payment calendar years. The claims volume adjustments aims to normalise the triangle for similar exposures across origin periods, while the earnings index, which measures largely wages and other forms of compensations, is used as a first proxy for claims inflation. Note that the earnings index shows significant year on year changes from 5% to 9%. Barnett and Zehnwirth [2] would probably recommend to add further parameters for the calendar year effects to the model.

# Page D5.36
ClaimsVolume <- data.frame(origin=0:6, 
  volume.index=c(1.43, 1.45, 1.52, 1.35, 1.29, 1.47, 1.91))
# Page D5.36
EarningIndex <- data.frame(cal=0:6, 
  earning.index=c(1.55, 1.41, 1.3, 1.23, 1.13, 1.05, 1))
# Year on year changes
round((1-EarningIndex$earning.index[-1]/EarningIndex$earning.index[-7]),2)
# [1] 0.09 0.08 0.05 0.08 0.07 0.05

dat <- merge(merge(dat, ClaimsVolume), EarningIndex)

# Normalise data for volume and earnings
dat$logvalue.ind.inf <- with(dat, log(value/volume.index*earning.index))

with(dat, interaction.plot(dev, origin, logvalue.ind.inf))
points(1+dat$dev, dat$logvalue.ind.inf, pch=16, cex=0.8)

Indeed, the interaction plot shows the various origin years now to be much more closely grouped. Only the single point of the last origin period stands out now. Christofides tests several models with different numbers of origin levels, but I am happy with the minimal model using only one parameter for the origin period, namely the intercept:Read more »

Reserving based on log-incremental payments in R, part II

2013-01-15T07:46:00.000Z

Following on from last week's post I will continue to go through the paper Regression models based on log-incremental payments by Stavros Christofides [1]. In the previous post I introduced the model from the first 15 pages up to section F. Today I will progress with sections G to K which illustrate the model with a more realistic incremental claims payments triangle from a UK Motor Non-Comprehensive account:

# Page D5.17
tri <- t(matrix(
  c(3511, 3215, 2266, 1712, 1059, 587, 340,
    4001, 3702, 2278, 1180,  956, 629,  NA,
    4355, 3932, 1946, 1522, 1238,  NA,  NA,
    4295, 3455, 2023, 1320,   NA,  NA,  NA,
    4150, 3747, 2320,   NA,   NA,  NA,  NA,
    5102, 4548,   NA,   NA,   NA,  NA,  NA,
    6283,   NA,   NA,   NA,   NA,  NA,  NA), nc=7))

The rows show origin period data, e.g. accident years, underwriting years or years of account and the columns present the development periods or lags. The triangle appears to be fairly well behaved. The last two years in rows 6 and 7 appear to be slightly higher than rows 2 to 5 and the values in row 1 are lower in comparison to the later years. The last payment of £1,238 in the third row stands out a bit as well.

Before I plot the data, I will transform the triangle into a data frame and add extra columns:

m <- dim(tri)[1]; n <- dim(tri)[2]
dat <- data.frame(
  origin=rep(0:(m-1), n),
  dev=rep(0:(n-1), each=m),
  value=as.vector(tri))

## Add dimensions as factors
dat <- with(dat, data.frame(origin, dev, cal=origin+dev, 
                            value, logvalue=log(value),
                            originf=factor(origin),
                            devf=as.factor(dev),
                            calf=as.factor(origin+dev)))

I am particularly interested in the decay of claims payments in the development year direction for each origin year on the original and log-scale. The interaction.plot of the stats package does an excellent job for this:

op <- par(mfrow=c(2,1), mar=c(4,4,2,2))
with(dat, interaction.plot(x.factor=dev, trace.factor=origin, 
          response=value))
points(dat$devf, dat$value, pch=16, cex=0.5)
with(dat, interaction.plot(x.factor=dev, trace.factor=origin, 
          response=logvalue))
points(dat$devf, dat$logvalue, pch=16, cex=0.5)
par(op)

Indeed the origin years 1 to 4 (rows 2 to 5) look quite similar and the decay of claims in development year direction appears to be linear on a log-scale from development year 1 onwards.

Based on those observations Christofides suggests two models; the first one will have a unique level for each origin year and a unique level for the zero development period. The parameters for development periods 1 to 6 are assumed to follow a linear relationship with the same slope \(s\):
\begin{align}
\ln(P_{ij}) & = Y_{ij} = a_i + d_j + \epsilon_{ij}
&\mbox{for } i,\,j \mbox{ from } 0 \mbox{ to } 6\\
\mbox{where } d_0 &= d,\quad d_j = s \cdot j
&\mbox{for } j > 0
\end{align}and \(\epsilon_{ij} \sim N(0, \sigma^2)\). The second model will be a reduced version of the above with only two levels for the origin years 5 and 6. Hence, I add four more columns to my data frame:Read more »

Reserving based on log-incremental payments in R, part I

2013-01-08T07:58:00.000Z

A recent post on the PirateGrunt blog on claims reserving inspired me to look into the paper Regression models based on log-incremental payments by Stavros Christofides [1], published as part of the Claims Reserving Manual (Version 2) of the Institute of Actuaries.

The paper is available together with a spread sheet model, illustrating the calculations. It is very much based on ideas by Barnett and Zehnwirth, see [2] for a reference. However, doing statistical analysis in a spread sheet programme is often cumbersome. I will go through the first 15 pages of Christofides' paper today and illustrate how the model can be implemented in R.

Let's start with the example data of an incremental claims triangle:

## Page D5.4
tri <- t(matrix(
  c(11073,  6427, 1839, 766,
    14799,  9357, 2344,  NA,
    15636, 10523,   NA,  NA,
    16913,    NA,   NA,  NA), 
  nc=4, dimnames=list(origin=0:3, dev=0:3)))

The above triangle shows incremental claims payments for four origin (accident) years over time (development years). It is the aim to predict the bottom right triangle of future claims payments, assuming no further claims after four development years.

Christofides model assumes the following structure for the incremental paid claims \(P_{ij}\):
\begin{align}
\ln(P_{ij}) & = Y_{ij} = a_i + b_j + \epsilon_{ij}
\end{align}where i and j go from 0 to 3, \(b_0=0\) and \(\epsilon_{ij} \sim N(0, \sigma^2)\). Unlike the basic chain-ladder method, this is a stochastic model that allows me to test my assumptions and calculate various statistics, e.g. standards errors of my predictions.
Read more »

Clone all your gists locally with R

2013-01-02T08:12:00.000Z

I really like gists as a quick way to include more lengthly code snippets into my blog posts. However, I am not a git user as such, and so I was quite concerned when I noticed that all my gists on this blog had vanished after Christmas. I suppose this was a result of Github's downtime on December 22nd.

Thankfully an email to the support guys at Github resolved the issue within a few hours. Still, I thought it might be a good idea to download my gists locally.

I can see all my gists as a JSON file online here: https://api.github.com/users/MYUSERLOGIN/gists

Thus, I downloaded the file and thanks to the RJSONIO package I was able to clone all my gists locally with a few lines of R:
Read more »

R in Insurance Conference, London, 15 July 2013

2012-12-19T06:42:00.000Z

The first conference on R in Insurance will be held on Monday 15 July 2013 at Cass Business School in London, UK.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

This one-day conference will focus on applications in insurance and actuarial science that use R, the lingua franca for statistical computation. Topics covered may include actuarial statistics, capital modelling, pricing, reserving, reinsurance and extreme events, portfolio allocation, advanced risk tools, high-performance computing, econometrics and more. All topics will be discussed within the context of using R as a primary tool for insurance risk management, analysis and modelling.

The intended audience of the conference includes both academics and practitioners who are active or interested in the applications of R in insurance.

The 2013 R in Insurance conference builds upon the success of the R in Finance and R/Rmetrics events. We expect invited keynote lectures by:

Professor Alexander McNeil, Department of Actuarial Science & Statistics
Heriot-Watt University
Trevor Maynard, Head of Exposure Management and Reinsurance, Lloyd's

We invite you to submit a one-page abstract for consideration. Both academic and practitioner proposals related to R are encouraged.

Details about the registration and abstract submission are given on the R in Insurance event web site of Cass Business School.

You can contact us via rinsuranceconference at gmail dot com.

The organisers, Andreas Tsanakas and Markus Gesmann, gratefully acknowledge the sponsorship of Mango Solutions.

Now I see it! K-means cluster analysis in R

2012-12-17T07:55:00.000Z

Of course, a picture on a computer monitor is a coloured plot of x and y coordinates or pixels. Still, I was smitten by David Sparks' posts on is.r(), where he shows how easy it is to read images into R to analyse them. In two posts [1], [2] he replicates functionality of image manipulation programmes like GIMP.

I can't resist to write about this here as well. David's first post is about k-means cluster analysis. One of the popular algorithms for k-means is Lloyd's algorithm. So, on that note I will use a picture of the Lloyd's of London building to play around with David's code, despite the fact that the two Lloyds have nothing to do with each other. Lloyd's provides pictures of its building copyright free on its web site. However, I will use a reduced file size version hosted on wikimedia.

The ReadImages package by Markus Löcher [3] allows me to load a jpeg-file into R. The R object of the images is an array, which has the structure of three layered matrices, representing the value of the colours red, green and blue for each x and y coordinate. I convert the array into a data frame, as this is an accepted structure by k-means and plot the data.

library("ReadImages")
url <- "http://upload.wikimedia.org/wikipedia/commons/6/6a/6414A_1_copy.jpg"
fn <- tempfile()
download.file(url, destfile=fn)
readImage <- read.jpeg(fn)

dm <- dim(readImage)
rgbImage <- data.frame(
                    x=rep(1:dm[2], each=dm[1]),
                    y=rep(dm[1]:1, dm[2]),
                    r.value=as.vector(readImage[,,1]),
                    g.value=as.vector(readImage[,,2]),
                    b.value=as.vector(readImage[,,3]))

plot(y ~ x, data=rgbImage, main="Lloyd's building",
     col = rgb(rgbImage[c("r.value", "g.value", "b.value")]), 
     asp = 1, pch = ".")

Running a k-means analysis on the three colour columns in my data frame allows me to reduce the picture to k colours. The output gives me for each x and y coordinate the colour cluster it belongs to. Thus, I plot my picture again, but replace the original colours with the cluster colours.Read more »