We cover few of the advanced pricing models for ratemaking in General Insurance and show how these uncover greater insights than basic pricing.

1. Advanced Pricing Practices - General
Insurance
Introducing Predictive Modeling
Revealing Insights

2. Value At Risk
Neural
Networks
Artificial
Intelligence
Generalized
Linear Models
Time Series
Analysis
Advanced
Pricing Using
Predictive
Modeling

4.  R is the free of cost, open-ware software available which can
equally fulfill the objectives of advanced pricing.
 R is the standard choice of software for the majority of statisticians
in the world due to it’s powerful results-generating capacity,
graphical outputs and thorough documentation.
 R is also the software upon which EMBLEM is developed so as to
minimize need for programming forTowers Watson clients.
 As such, Institute and Faculty of Actuaries along with Casualty
Actuarial Society regularly publishes developments in R for
actuaries; especially by Lloyds research specialists.
 Scaling option for massive computing available now with the
advent of H20 package. Centralized ‘caret’ package for 147+ models
of predictive modeling and machine learning as well.

5. Definition
Data
Develop
Results
Define objectives
of the predictive
modeling exercise
Understand and
ensemble the data
Develop the
Predictive Model
Reach Results and
keep them under
monitoring

6. Burning Cost (BC)
1) Rating Variables
2) IBNR Loss
Development
Factors
Classification
1) Premium for each
Product Type
2) Premium for
additional benefits
Modifications On
BC
1) Loadings such as
profit margin and
inflation.
2) Adjustments for
catastrophes and
deductibles
Market
Premium
The Gross Premium to be
charged to the policyholder

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•Generalized Linear Models (GLMs) have been applied in R
•Time Series analysis has been carried out:
•Decomposition of the data
•Forecasting - ARIMA models
•Value at Risk (VaR)
•We have implemented VaR, GLM and Time Series, leaving Artificial
Intelligence ( like Fuzzy Logic and Neural Networks) for the future.
•All these models have been implemented on real but fully
anonymized dataset.

8. Objective 1
GLM is not strictly a calculator, rather
it is a ‘pricing generator’ that captures
significant trends and ignores random
noise in the data. It is a guide that
when quoting prices, know the
premium that you should be quoting
but some deviation can be allowed if
it is adequately justified.
Agenda of Predictive Modeling- Objectives
Covered

9. GLM is not strictly a calculator, rather it is a
‘pricing generator’ that captures significant
trends and ignores random noise in the data. It is
a guide that when quoting prices, know the
premium that you should be quoting but some
deviation can be allowed if it is adequately
justified.
Objective 1
Objective 2
Time Series reveals insights into
the patterns of the data generated
over time.The second purpose is to
forecast for the next 3 years how
much monthly claim costs incurred
the company should expect.

10. Objective ofVaR is to expose the
5% worst-case threshold limit on
losses, which is the loss amount
that is likely to be exceeded by
the 5 % worst-case losses.
GLM is not strictly a calculator, rather it is a
‘pricing generator’ that captures significant
trends and ignores random noise in the data. It
is a guide that when quoting prices, know the
premium that you should be quoting but some
deviation can be allowed if it is adequately
justified.
Put the detail about your 2nd
quality here. Put detail for the
2nd quality here. Put the detail
for the 2nd quality here. Put
the detail for here. Put the
detail for here. Put the
details here…
Objective 3
Objective 1
Objective 2

11.  Time series is a sequence of data points
measured usually at successive points in time
spaced at uniform time intervals.
 ARIMA (Auto Regressive Integrated Moving
Average) model of time series has been
employed for the forecasting since it is the
standard practice.

12.  Decomposition can be very valuable for the
management due to its revealing insights.
 ‘observed’ shows the actual claims data pattern.
 ‘trend’ shows the long term pattern that the
 ‘seasonal’ shows the medium and short term
pattern the data follows
 patterns that do not follow under seasonal and
trend are given as ‘random’ patterns.

13.  Decomposition of motor claims incurred amounts over 5 years is as shown below.
 The long term trend shows underwriting cycle and seasonal shows drop in claims in year
end for every year.

14.  Forecasting is done through employing ARIMA
(Auto Regressive Integrated Moving Average)
Model of time series.
 It is done for 3 years 2014, 2015 and 2016
respectively.
 The Claims Forecast is then elaborated side by
side with Upper Estimate and Lower Estimate
respectively.
 The Upper and Lower estimates are based on
85% Confidence Interval and are provided as
sensitivity test for the Claim Forecast figures.

15.  The forecasts are shown pictorially as follows:

16.  It express the relationship between an
observed response variable and a number of
predictor variables.
 The process that we followed during this
predictive modeling exercise can be shown as
follows:Define the objectives
Understand
and ensemble
the data
Develop the
GLM predictive
model
Reach Results
and monitor
the results

17.  Gamma distribution has been employed in the model
with a logarithmic link function.
 The relativity factors or predictor variables used here in
the model are:
 Product Name
 Driver Age
 Driver Nationality
 Branch Name
 Age of Car
 ManufacturedYear
 Seat Capacity
 Luxury or non luxury
 Agency or no agency
 Bands of Sum Assured
 Body type
 Vehicle Make

18.  The model produces probability p-value for each variable and
coefficient to make it possible to select only the significant factors
and coefficients and ignore the rest which lead to random noise.
This is in line with our objective of finding the most ‘parsimonious’
model which is not over-fitted or under-fitted to data.
 All ten variables were deemed ‘significant’ statistically as none of
the variable gave a probability p-value of more than 5%.
 The p-value should be less than 5% in order for the coefficients to
be significant. Only significant coefficients were taken into
account.

19. -
10,000,000
20,000,000
30,000,000
40,000,000
50,000,000
60,000,000
-
500
2,000
5,000
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
500,000
1,500,000
TotalAmountswithinpremiumbands
Premium amount bands
Actual Premium data and GLM premium distribution
Actual Data
GLM Model Output

21.  GLM should not be taken lightly. This is because
GLM has become part of the general insurance
actuarial standard suite of models on an
international level.
 That being said, GLM model is a guide when
quoting prices for new motor insurance policies.
If the underwriter faces unique circumstances
and can adequately justify deviation of premium
from the model it should be allowed, as far as a
reasonable explanation can be given.

22.  Value at Risk or VaR answers the question “how much do you stand to lose, over
a certain period and with a certain probability?”
 Historical simulation is a useful measure of calculating VaR especially because it
assumes no specific distribution; it simply lets data tell the story. Given that we
have 5 years claims incurred data, it is more than sufficient and credible.
 At first, return series are generated using the natural logarithm of present claim
over previous claim. This generates the volatility that should be taken into
account in theVaR calculation.
 In estimating VaR, volatility is the central component as it is volatility that
condenses the trend of figures for respective time period into a quantifiable
position. The other determinants are the specification of confidence interval and
time period.
 Historical simulation method simply reorganizes actual historical returns, putting
them in order from worst to best. It then assumes that history is a good predictor
of future losses.

23.  This histogram of Return Series for claims incurred of Motor Claims data
over the past 5 years 2009-14 is shown below:
0
500
1000
1500
2000
2500
3000
3500
Frequency
Histogram of Return Series

24.  The two ‘spikes’ are outliners in the data which have not been incorporated in
the calculations. Overall, the histogram points our attention to estimating
the worst 5% losses which can be determined from its tail.
 Using Confidence Interval of 95% and duration of one year, we are 95% sure
that the 5% worst case losses will exceed the amount of AED 342,063 over
one year. Kindly note, that we only estimate the threshold limit, which is the
amount that will be exceeded. VaR does not tell us how worse the loss will
get once it exceeds the threshold amount.
 Back-testing this result, data tells us that 6% of claims are those claims that
have amount of AED 300,000 and beyond.
 VaR is meant to guide management and is therefore no replacement for
active managerial understanding. However, it also reveals an important
insight into the risk that the company is incurring and is therefore a potent
risk management tool.

25. Conclusions- How to maximize ability to introduce
these models in emerging markets
Mathematical Integrity
Using powerful software like R
User-Friendly, Succinct and Results-
Oriented Reporting
Continuous Monitoring
Customer

26.  What we have developed in this presentation
is only ‘the tip of the iceberg’ of what can
actually be done. Once we generate enough
momentum, we can introduce a library of
other practically implementable General
Insurance Pricing, Reserving as well as ERM
models.
 “The world is your oyster; go and discover
your pearls’.

27. Stochastic
Reserving
Artificial
Intelligence for
Pricing, Reserving
and ERM
ERM models such
as Monte Carlo,
ExtremeValue
Theory etc
Catastrophe
Modeling
A lot of other
diverse areas
Advanced Pricing
Basic Pricing
Basic Reserving Miscellaneous Such as
StressTesting, Product
Approval and FCR reports