We review basic reserving methodologies for reserving general insurance like lag analysis and chain ladder. We then move forward to consider multiple stochastic loss reserving models in detail and show how they uncover more insights than basic reserving models.

1. Stochastic Loss Reserving
Introduction to Stochastic Loss Reserving for General Insurance Valuations

2. Introduction
• Loss reserving covers Incurred but Not Reported
(IBNR) claims. These reserves are usually estimated
based on historical claims paid based on
accident/reporting patterns.
• In the past a point estimator for the reserves was
sufficient. New regulatory requirements (such as
Solvency II and other risk management regimes)
foster stochastic methods for loss reserving.
• Stochastic Reserving has been applied on real but
completely anonymized data using statistical
software R.

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Lag-Factor Practice of
IBNR Reserving

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IBNR reserve is shown
here as calculated by LAG
ANALYSIS.
Countdown
to Lag
Analysis
Practice

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on
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Current Reserving Practice
• Here IBNR Reserve was based on Lag analysis.
One of the major aspects for unpaid claims
estimation is the appropriate assessment of
reporting lag. We have analyzed the lag between
the incident date and the reported date where the
data indicated the following reporting lags (by
accident year):

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Current Reserving Practice
• This can be illustrated as follows:

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Current Reserving Practice
• Based on the lag analysis, Gross IBNR was
determined as follows:

18. • Chain Ladder can be readily applied on
and the following diagram elaborates
on the methodology behind
triangulation:

19. •The Paid Claims triangle on accident quarter to reported quarter basis can be
shown below (Due to the magnitude, the triangle will be shown in 2 parts):

21. • This claim development triangle can be visualized as follows:
-
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
50,000
AED'000
Claims Development Chart 2008-2013
0 Quarter
1 Quarter
2 Quarter
3 Quarter
4 Quarter
5 Quarter
6 Quarter
7 Quarter
8 Quarter
9 Quarter
10 Quarter
11 Quarter
12 Quarter
13 Quarter
14 Quarter

22. Applying the basic Chain Ladder methodology on this triangle, the total Gross IBNR
comes out to be AED 64, 577,062.

23. Stochastic Loss
Reserving
Welcome to the Future!

24. The Future begins NOW!

25. Why Stochastic Loss Reserving?
– The following delivers reasons for why we should adopt stochastic reserving:
• Computer power and statistical methodology make it possible
• Provides measures of variability as well as location (changes emphasis on best
estimate)
• Can provide a predictive distribution
• Allows diagnostic checks (residual plots etc)
• Useful in Dynamic Financial Analysis (DFA)
• Useful in satisfying Own Risk Solvency Assessment (ORSA) under different risk
management regimes
•
– As per Richard Verrall of CASS Business School, who is the leading authority in
stochastic loss reserving:
• “In recent years, a lot more attention has been given to the possible differences
between the reserves and the actual outcome in terms of the claims paid. And also,
there is considerable interest in the variability of the reserves from year to year: as
more information becomes available, the estimates of what will have to be paid in
claims may change. This is very important because it influences the amount of
capital that companies are required to hold to ensure their continuing solvency. The
capital that is required also shows to investors and management how profitable the
business is (or different parts of the business are). For all these reasons, a lot more
attention has been given to the likely variability of the claims reserves, as well as the
actual amount held in these reserves.”

26. Why Stochastic Reserving?
– Stochastic reserving does not just give us the best estimate,
it also provides us with the variability in claims reserve. The
variability of a forecast is given as prediction error or
standard error, where prediction error is:
• Prediction Error= (Process Variance + Estimation Variance)^1/2
– The following stochastic loss reserving models have been
applied:
• Mack Model
• Bootstrap Model
• Generalized Linear Model (GLM) utilizing Over Dispersed
Poisson
•
– Kindly note that Mack produces results that are very close
to Chain Ladder and GLM using Over Dispersed Poisson
distribution produces same results as Mack.

27. Mack Model
– Thomas Mack published in 1993 a method
which estimates the standard errors of the
chain-ladder forecast without assuming any
particular distribution.
•
– The Mack-chain-ladder model gives an
unbiased estimator for IBNR (Incurred But
Not Reported) claims. The Mack-chain-
ladder model can be regarded as a weighted
log-linear regression through the origin for
each development period. Prediction Error
is the total variability in the projection of
future losses by the Mack Method.

28. Mack Model-Results
The total results are depicted below:
Prediction Error helps us to estimate that we are 95% confident that the true IBNR
value lies around between AED 40 million and AED 89 million.

29. Mack Model- Model Diagnostics
– The residual plots show the
standardized residuals against fitted
values, origin period, calendar period
and development period. All residual
plots should show no pattern or
direction other than broadly
converging towards zero. Slight
deviation is expected and is not a
cause for concern. Kindly see next
slide for the residual plots.

30. Mack Model- Model Diagnostics

31. Bootstrap Model
– The Bootstrap model uses a two-stage
bootstrapping/simulation approach following the
paper by England and Verrall [2002]. In the first stage
an ordinary chain-ladder methods is applied to the
cumulative claims triangle. From this we calculate
the scaled Pearson residuals which we bootstrap R
times to forecast future incremental claims
payments via the standard chain-ladder method. In
the second stage we simulate the process error with
the bootstrap value as the mean and using the
process distribution assumed. The set of reserves
obtained in this way forms the predictive
distribution, from which summary statistics such as
mean, prediction error or quantiles can be derived.

32. Bootstrap Model
•Bootstrap uses Gamma Distribution in arriving at its estimates of
IBNR reserves.
•The results of simulating bootstrap replicates to generate estimates
for IBNR can be depicted as a histogram of frequency as below:

33. Bootstrap Model
The mean ultimate claims that have been simulated can be made
evident as follows:

34. Bootstrap Model- Results
•The total results can be displayed as follows:
•Through utilizing prediction error, we can be 95% confident that the true
IBNR value lies between around AED 58 million and AED 104 million.

35. Generalized Linear Model
– Although GLM is mainly used in pricing of general
insurance premiums, GLMS have found their way into
reserving as well. The GLM takes an insurance loss triangle,
converts it to incremental losses internally if necessary,
and fits the resulting loss data with a Generalised Linear
Model where the mean structure includes both the
accident year and the development lag effects. The GLM
also provides analytical methods to compute the
associated prediction errors, based on which the
uncertainty measures such as predictive intervals can be
computed.
– Only the Tweedie family of distributions are allowed, that
is, the exponential family that admits a power variance
function V (u) = up. For the purposes of stochastic loss
reserving, the distribution of Over-Dispersed Poisson was
utilized, especially since this choice of distribution will lead
to same mean figure for IBNR as provided in Mack.

36. Generalized Linear Model
• Total results can be displayed as follows:
•For the purposes of stochastic loss reserving, the distribution of Over-
Dispersed Poisson was utilized, especially since this choice of distribution will
lead to same mean figure for IBNR as provided in Mack.
•This shows, amongst others, that we are 95% confident that the true IBNR
reserve value lies around between AED 32 million and AED 98 million.

37. Conclusions for our Business
Stochastic Modeling is the way forward!

38. 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

39. Conclusions
– Applying triangulation method of chain ladder does not just
improve deterministic reserving but also enables stochastic
reserving to be introduced through comparison of the results of
Chain Ladder.
• “I believe that stochastic modelling is fundamental to our
profession. How else can we seriously advise our clients and our
wider public on the consequences of managing uncertainty in the
different areas in which we work?”
• - Chris Daykin, Government Actuary, 1995
• “Stochastic models are fundamental to regulatory reform”
• - Paul Sharma, FSA, 2002

40. References
• Stochastic Claims Reserving in General Insurance
England, PD and Verrall, RJ (2002)
• Claims Reserving in R-Markus Gesmann
• Claims Reserving with R: package Vignette-Markus
Gesmann, Dan Murphy and Wayne Zhang

41. Thank You for Your
Attention!