We are excited to release a new paper on aggregating neural network predictions with a focus on actuarial work. The paper examines the stability of neural network predictors at a portfolio and individual policy level and shows how the variability of these predictions can act as a data-driven metric for assessing which policies the network struggles to fit. Finally, we also discuss calibrating a meta-network on the basis of this metric to predict the aggregated results of the networks.
Here is one image from the paper which looks at the effect of “informing” the meta-network about how variable each individual policy is.
If you would like to read the paper, it can be found here:
The Human Mortality Database (link) is one of the best sources of demographic data that is publicly available. In addition to their regular reporting across about 40 countries, the curators have now added a special time series of weekly death data across 13 countries to enable the tracking of COVID19 deaths, and the effect on weekly mortality rates. In their usual fashion, the HMD have provided the data in an easy to use csv file which can be downloaded from the website.
Rob Hyndman (whose work on time series forecasting I have learned much from over the years and whose R packages and textbook I use/mention in this blog) posted today about this new data source on his excellent blog (https://robjhyndman.com/hyndsight/excess-deaths/). He shows plots of the excess deaths for all 13 countries.
I was wondering how one might derive a predictive interval for these weekly mortality rates, and to what extent the COVID19 mortality rates would lie outside a reasonable interval. What follows is a rough analysis using time series methods. A quick inspection of the rates for the UK shows that there are strong seasonal features, as shown in the image below.
Interestingly, the data dip and then recover around week 13 each year, probably due to reporting lags around the Easter holidays. Other similar effects can be seen in the data. To produce reasonable forecasts, one approach would be to attempt to model these seasonal issues explicitly.
Thanks to the excellent forecast package in R, this is really easy. First, we show a season and trend (STL) decomposition of the these data (excluding 2020). For details on this technique, see this link.
The plot shows quite a strong seasonal pattern which is often characterized by dips and recoveries in the data. Overall, the trend component seems to have increased since 2010, which is a little puzzling at first glance, as mortality rates in the UK have improved for most of the period 2010-2019, but is probably due to an aging population.
One could now use the STL forecasting function (forecast::stlf) to produce forecasts. Here, I have rather chosen to fit a seasonal ARIMA model (link). The model specification that the forecast::auto.arima function is an ARIMA(2,0,1)(1,1,0) model.
Finally, we are ready to forecast! In this application, I have used confidence levels of 95% and 99.5% respectively. Plotting the 2020 data against this interval produces the following figure.
It can be seen that the 2020 weekly mortality rates fall dramatically outside even a 99.5% interval. It is probably not too surprising that an uncertainty interval calibrated on only 10 years of data is too narrow, but the extent to which this has occurred is dramatic!
This analysis is very rudimentary and could be improved in several ways: obviously the distributional assumptions should be amended to allow for larger shocks, and more advanced forecasting would allow for sharing of information across countries.
I am very grateful to the Casualty Actuary Society’s committee that awarded my 2018 paper “AI in Actuarial Science” the 2020 Hachemeister prize. I hope that the methods discussed in the paper eventually make an impact on P&C actuarial practice! If you want to read the paper, please find it here. One of my favorite images from the paper is pasted below and shows the results of a convolutional autoencoder fit to telematics data.
We are excited to share a new paper on “Discrimination-Free Insurance Pricing” written by Mathias Lindholm, Andreas Tsanakas, Mario Wüthrich and a small contribution from myself. In this paper, we present a general method for removing direct and indirect discrimination from the types of models in common use in the insurance sector (GLMs) as well as more advanced machine learning methods.
One of my favorite plots from the paper shows a comparison of prices produced using a neural net with our method applied to the results.
We would like to hear your feedback and the paper can be downloaded here:
The call for abstracts is open for the first Insurance Data Science Conference
– Africa at the Sandton Convention Centre, 20 April 2020, which is jointly
organized by the Actuarial Society of South Africa, QED Actuaries and
Consultants and the University of the Witwatersrand. The invited keynote
speakers are Mario Wüthrich (RiskLab, ETH
Zürich) and Marjorie Ngwenya (ALU School of Insurance, past President
of the Institute and Faculty of Actuaries).
We are inviting abstracts in the areas of insurance
analytics, machine learning, artificial intelligence, and actuarial science.
Please send your abstract by 29 February 2020 to: firstname.lastname@example.org
Your submission should include:
affiliation of the speaker
Email address of
Title of the
Abstract of 10 to
20 lines and not more than 5 references
Note: The international version
of this conference has been held in European cities for the past 7 years and
returns to London in 2020. For more information, please visit: https://www.insurancedatascience.org/
One of the most inspiring events I have attended was the Insurance Data Science Conference held in Zurich this year.
I am very excited to announce that on 20 April 2020 we will hold an affiliated event in South Africa, which will be organized by the Actuarial Society of South Africa, QED Actuaries & Consultants, and the University of the Witwatersrand. The conference website is here:
The call for abstracts is open and we look forward to receiving your submission.
Finally, the 2020 event in Europe will be held in London at the Cass Business School. The call for abstracts has just gone out and the website is here:
About a week ago, I attended the second Insurance Data Science Conference held at ETH Zürich. On a personal note, I am very grateful to the conference organizers for inviting me to give a keynote, and my deck from that presentation is here. Making the conference extra special for me was the opportunity to meet the faculty of ETH Zürich’s RiskLab, who have written some of the best textbooks and papers on the actuarial topics that I deal with in my professional capacity.
This was one of the best organized events I have attended, including the beautiful location of the conference dinner at the Zürich guild house (shown below), and the hard choices of deciding between simultaneous sessions at the conference. It was great to see the numerous insurance professionals, academics and students who were present – the growth in the number of conferences attendees from previous years is witness to the huge current interest in data science in insurance, which will I am sure will help create tangible benefits for the industry, and the policyholders it serves.
In this post I will discuss some of the interesting ideas presented at the IDSC 2019 that stand out in my memory from the conference. If any of these snippets spark interest, then the full presentations can be found at the conference website here.
Evolution of Insurance Modelling
It is interesting to observe the impact on modelling techniques
caused the availability of data at a more granular level than previously, or
due to a recognition of the potential benefits of better exploiting traditional
data. I would categorize this impact as a move towards more empirical modelling,
but still framed within the classical actuarial models, and I explain this by
examining some of the standout talks for me that fell into this category. Within
my talk, I showed the following slide, which discusses the split between those
actuarial tasks driven primarily by models, versus those driven by empirical relationships
found within datasets. Many of the talks I discuss cover proposal to make tasks
that are today more model driven, more empirically driven.
One of the sessions was structured with a focus on reserving
techniques. Alessandro Carrato presented on an interesting technique that
adapts the chain ladder method within an unsupervised learning framework. This technique
is used for reserving for IBNeR on reported claims and works by clustering
claims trajectories in a 2d spaced comprised of claims paid and outstanding loss
reserves. Loss development factors are then calculated using development
factors calculated from the more developed claims in each cluster. Thus, the traditional
approach of finding “homogenous” lines of business, which is usually done subjectively,
is here replaced by unsupervised learning. Another reserving talk, by Jonas
Crevecoeur, also investigated the possibility of reserving at a more granular level
using several GLMs, which were shown to reduce to more traditional techniques depending
on the choice of GLM covariates.
Within the field of mortality modelling, Andrew Cairns
presented on a new dataset covering mortality in the UK split by small geographic
areas. This dataset also includes several static variables describing the circumstances
of each of these areas, such as deprivation index, education, weekly income,
nursing homes, allowing for the modelling of granular mortality rates depending
on these covariates. This presentation took a very interesting approach –
firstly, an overall national mortality rate was calculated, and then the
mortality rate in each area was compared to the national rate in a typical “actual
versus expected” analysis. Models were then estimated to explain this AvE analysis
in terms of the covariates, as well as in terms of the geographic location of
each area. An interesting finding was that income deprivation is an important indicator
of excess mortality at the older ages, whereas unemployment is more important at
the younger ages.
Another talk on mortality modelling was given by Andrés Villegas, who cast traditional mortality models into what I would call a feature engineering context. In other words, many traditional mortality models, such as the Cairns-Blake-Dowd model can be expressed as a regression of the mortality rate on a number of features, or basis functions which represent, different combinations of age, period and cohort effects. The method basically proceeds by setting up a very large number of potential features, and then selecting these using the grouped lasso technique (which gives zero weight to most features i.e. performs feature selection). A very similar idea has appeared in the reserving literature from Gráinne McGuire, Greg Taylor and Hugh Miller (link). This talk epitomized for me the shift to more empirical techniques, within a field that has traditionally been defined by models and competing model specifications(Gompertz vs Kannisto, Lee-Carter vs Cairns-Blake-Dowd etc).
Keeping it safe
A topic touched on by some speakers was the need to manage
new, emerging risks arising due to advanced algorithms and open source software.
Jürg Schelldorfer presented an excellent view of how to apply machine learning models
within a highly regulated industry such as insurance. Some of his ideas were to
focus on prediction uncertainty, and to provide questions to be answered when
peer reviewing ML models. I highly recommend this presentation if you are going
on the ML journey within an established company!
Jeffrey Bonh also spoke about this theme, emphasizing “algorithmic
risks”, which are risks arising due to poor data used to calibrate ML
algorithms, or due to the risks of malpractice during algorithmic design and calibration.
Within this section, I would also mention the amazing morning keynote by Professor Buhmann, who presented on an alternative to the paradigm of empirical risk minimization, used often to train ML models. The extent of the knowledge of ML theory shown in this talk was breath-taking, and I am excited to delve into Professor Buhmann’s work in more detail link. The lesson here for me was that it is a mistake to assume that ML methodology is “cut and dried”, and that by building more knowledge about alternative methods, one can hopefully understand some of the risks implied by these techniques.
R – the language for insurance data science
The IDSC began life as the R in Insurance conference, and in
this respect, many interesting talks covered innovative R packages. Within the
sessions I attended, Daphné Giorgi presented an R package used for simulating human
populations based on individuals, which showed excellent performance due to the
implementation of some of the algorithms in C++. Kornelius Rohmeyer presented a
very promising package called DistrFit, which, as the name implies, is helpful for
fitting distributions to insurance claims. This package is a very neat Shiny
app, which automates some of the drudge work when fitting claims distributions
in R. I hope this one gets a public release soon! Other notable packages are Silvana
Pesenti’s SWIM package which implements methods for sensitivity analysis of
stochastic models and the interesting sue of Hawke’s processes by Alexandre
Boumezoued for predicting cyber claims.
I would also mention the excellent presentation on
TensorFlow Probability by Roland Schmid. TF Probability offers many possibilities
of incorporating a probabilistic view into Keras deep learning models (amongst other
things) and it is exciting that RStudio is in the process of porting this
package from Python to R.
The above is a sample of the excellent talks presented
(biased towards my own interests), and I have not done justice to the rest of
the talks on the day.
I look forward to IDSC 2020 and wish the organizers every
success as this conference grows from strength to strength!
Very excited to be attending the Insurance Data Science conference at ETH Zurich on Friday. I will be giving a keynote presentation on the state of the art in applying deep learning to actuarial problems. If you are there, then it would be great to meet. My slides are available at the link below: