1. NZ Actuarial Conference
The next step in performance monitoring – Stochastic monitoring (and reserving!)
NZ Actuarial Conference
November 2010

2. Agenda Monitoring of claim experience Adding some confidence
Stochastic reserving
Questions…

3. Agenda Monitoring of claim experience Adding some confidence
Stochastic reserving
Questions…

4. What is monitoring? Wikipedia definition: Actuarial interpretation:
The act of listening, carrying out surveillance on, and/or
The act of detecting the presence of signals
Actuarial interpretation:
To identify when experience is contrary to expected such that appropriate action can be taken when required.

5. Case study
Consider a Workers’ Compensation portfolio with periodic income benefits
Focus on the model of payments per active claim
Initial model established at December 2008 and monitored quarterly until March 2010
Consider a WC portfolio with periodic income benefits.
We’ll concentrate on the level of Payments per active claim, where the PPAC is defined as the amount of periodic income payments received in a payment quarter for each “active” claim in that quarter
A claim is counted as “active” once in each quarter if it receives a payment for periodic income benefits

6. Case study – basic monitoring
Actual has increased rapidly at Dec 09 and Mar 10, but is it significant or simply random variation?

7. Case study – basic monitoring
Detailed results
Tabulated results

8. Case study – initial model
Chart shows average of the last 4 payment quarters compared to the selected December 2008 model

9. Case study – basic monitoring
Is this volatility unusual? Is a change in assumption indicated?

10. Case study – 5 quarters on
Significant?
Chart shows average of the 5 payment quarters to Mar 2010 compared to the selected December 2008 model

11. Case study – combined
Was it ever significant?

12. Case study Difficult to determine “real change” vs random variation
Often reliant on valuation actuary’s “judgment” in how best to respond
Impact of judgement is not assessable at the time, and
Generally not subject to hindsight review

13. Agenda Monitoring of claim experience Adding some confidence
Stochastic reserving
Questions…

14. Step 1 – use all the data Traditional approach Stochastic approach
Development quarter
Development quarter
Accident quarter
Accident quarter
Data used to set assumptions
Data used to set assumptions

15. Step 1 – use all the data Note
The relative smoothness and sensible shape of the curve, and
The variability of an individual development quarter even using all the data!

16. Step 2 – break development curve into sections
Each section is controlled by a single parameter allowing it to move up or down over time

17. Step 3 – plot the history of each section over time and project
Projection
Strong SI
Take a slice of the accident qtr, development qtr curve – and look at the time series by payment quarter
As the chart shows there have been shifts in the experience over time - which the GLM is readily able to capture
The early part of the development curve has moved up and down over time
The projection of these payment parameters completely determines the valuation

18. Step 4 – monitor parameter experience until the next valuation
Inter-valuation experience
Projection
Strong SI
By 2nd quarter there is a statistically significant difference between the projection and experience. Clear evidence for assumption change

19. Another eg – development quarters 20 plus
Each section is controlled by a single parameter allowing it to move up or down over time

20. Step 3 – again, plot the history of each section over time and project
Projection
Slight SI
Slight upward trend in fitted curve indicates 0.6% p.a. SI consistent across time
Typically this would be missed by non-stochastic valn methods

21. Step 4 – monitor parameter experience until the next valuation
Inter-valuation experience
Projection
Slight SI
Combined, the last two quarters show that there is a statistically significant difference between the projection and experience.

22. Step 4 – last 2 quarters combined
Fitted falls outside the confidence interval
Having combined last 2 estimates, giving a narrower confidence interval we see that the fit clearly falls outside the 95% CI
Ie, a 5% level of significance hypothesis test concludes that the experience has altered

23. Agenda Monitoring of claim experience Adding some confidence
Stochastic reserving
Questions…

24. Why use stochastic (GLM) reserving models?
Allows stochastic monitoring to be carried out
...which improves understanding of underlying trends
...and gives earlier warning of changes
More likely to produce more accurate valuations
...less prone to bias
...able to find underlying trends not readily observable by the human eye
It’s easier and faster (except the first time)!

25. Dealing with some common misconceptions
Fantasy
Time consuming
Black box and difficult to understand
The results are not transparent
Can’t apply judgement
Reality
Like all modelling significant upfront establishment required. Once established more efficient than traditional methods
Output provides additional insights
Professional judgement remains a key feature
Stochastic reserving follows exactly the same path with the same input and output as traditional models
Help is available!
Don’t have to licence additional software to do it (most organisations have sas)

26. Reserving Triangle Data Select model
(e.g. Number of claims, PPCI’s, PPAC’s)
Select model
Projection of cash flows
I&D, Gross & Net
Summary results 26

27. Reserving Triangle Data Select model Traditional
e.g. Excel spreadsheet
Triangle Data
(e.g. Number of claims, PPCI’s, PPAC’s)
Select model
Projection of cash flows
I&D, Gross & Net
Summary results
Vol weighted averages
recent diagonals
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet 27

28. Reserving Triangle Data Select model Traditional Stochastic
e.g. Excel spreadsheet
Triangle Data
(e.g. Number of claims, PPCI’s, PPAC’s)
Select model
Projection of cash flows
I&D, Gross & Net
Summary results
e.g. Excel to SAS, convert to columns
Vol weighted averages
recent diagonals
Fit GLM using SAS or other statistical software
e.g. Excel spreadsheet
e.g. SAS output to Excel
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet
e.g. Excel spreadsheet 28

29. First time GLM fitting procedure
Identify model structure
Fit saturated model
Simplify development curve shape
Simplify payment or accident year trends
Add seasonal patterns
Search for interactions
Review output and fit diagnostics
Triangles of fitted values and comparison of actual v fitted
AvE summaries by development period, payment period and accident period

30. Simplify development curve shape30

31. Some standard diagnostics31

32. Second and subsequent valuations
Run previous model on updated data set
Review diagnostics on updated model
Adjust model when necessary

33. Back to the case study... Conventional view of GLM fit vs 4 qtr avg

34. Conventional view of GLM fit vs 4 qtr avg plus traditional model fit

35. Conventional view of GLM fit vs 4 qtr avg plus traditional model fit
Traditional methodology has underestimated the trends

36. Conventional view of GLM fit vs 4 qtr avg plus traditional model fit
The traditional fit under-estimated the tail by about 5% (excl SI)

37. Agenda Monitoring of claim experience Adding some confidence
Stochastic reserving
Questions…

38. Key points
Stochastic monitoring enables the user to readily determine changes in experience
Earlier warning than traditional model
Identify when response required
Stochastic models for reserving readily identify trends over the entire triangle of experience
Less prone to bias
Better able to capture underlying trends in experience
Ability to analyse the data by numerous variables to check the model fit