Advanced Pricing Practices - General Insurance

Introducing Predictive Modeling

Revealing Insights

This Illustration describes the various facets of Advanced Pricing employed as current practice by the leading actuarial consultancies.

Value At Risk

Neural Networks

Artificial Intelligen

ce

Generalized Linear

Models

Time Series Analysis Advanced

Pricing Using

Predictive Modeling

Software used throughout the world

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 for Towers 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.

R------State-of-the-Art Statistical Software

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

Predictive Modeling Process-Flow

Basic Ratemaking

Burning Cost (BC)1) Rating Variables

2) IBNR Loss Development

Factors

Classification1) Premium for each

Product Type2) 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.

Steps Taken to Implement Advanced Pricing

Objective 1GLM 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

PREDICTIVE MODELING

Agenda of Predictive Modeling- Objectives Covered

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 2Time 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.

AGENDA-PREDICTIVE MODELING

Objective of VaR 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.

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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…

AGENDA- PREDICTIVE MODELING

Objective 3

Objective 1

Objective 2

Time Series Analysis

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.

Time Series Analysis

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.

Time Series Analysis 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.

Time Series Analysis 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.

Time Series Analysis The forecasts are shown pictorially as follows:

Generalized Linear Models

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

Generalized Linear Models

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 Manufactured Year Seat Capacity Luxury or non luxury Agency or no agency Bands of Sum Assured Body type

Vehicle Make

Generalized Linear Models

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.

Generalized Linear Models

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00 5,0

00

15,00

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30,00

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45,00

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60,00

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75,00

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90,00

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200,0

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275,0

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1,500

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10,000,000

20,000,000

30,000,000

40,000,000

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Actual Premium data and GLM premium distribution

Actual DataGLM Model Output

Premium amount bands

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l Am

ount

s w

ithin

pre

miu

m b

ands

Generalized Linear Models

Generalized Linear Models - Recommendations

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.

Value At Risk (VaR) 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 the VaR 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.

Value At Risk (VaR) 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

Histogram of Return Series

Freq

uenc

y

Value At Risk (VaR) 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.

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

Conclusions

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’.

Stochastic Reserving

Artificial Intelligence for

Pricing, Reserving and

ERM

ERM models such as Monte Carlo, Extreme Value Theory

etc

Catastrophe Modeling

A lot of other diverse areas

What we do in emerging markets compared to what we are actually capable of doing

Advanced Pricing

Basic PricingBasic Reserving Miscellaneous Such as

Stress Testing, Product Approval and FCR reports

Thank You for your attention.