Videos marked with an (*) contain discussion of new content in ICRFS-Plus™ 12.

If for any reason you are unable to view the training or demonstration videos, please contact our support staff at **support@insureware.com** and we will arrange to send you a copy of the videos on CD-ROM. You will be able to run the videos from the CD.

The training videos should be used for __hands on__ training. We suggest you run the videos on a separate computer using a data projector, and train as a group.

The only way you will learn all the new concepts and be able to exploit all the immense benefits is by using the system. Experiential learning is imperative.

It is important that you study the videos in sequential order as set out below.

# Table of Contents

1. Introduction to ICRFS-Plus™ 12 and modelling modules

2. Modelling using the Link Ratio Techniques and Extended Link Ratio Family modelling framework

3. Introduction to the Probabilistic Trend Family modelling framework

4. Modelling real data (CTP) in the PTF modelling framework

5. TG CS5: heteroscedasticity and varying parameters

6. TG ABC: modelling wizard, simulations, and release of capital as profit

7. Importing of data from other applications and COM Automation

8. Further PTF Modelling Examples

- 8.1 CompA and WCom
- 8.2 SDF and more on WCom
- 8.3 Case Study LR High
- 8.4 Accident year heteroscedasticity
- 8.5 Even and uneven triangle groups

11. Clusters and MPTF Concepts

12. Capital Management of long tail liabilities

14. Other applications of the MPTF modelling framework

15. The Bootstrap: how it shows the Mack method doesn't work

## 8. Further PTF modelling examples

# 8.1 CompA and WCom

The first triangle group we examine is CompA. This data is quite volatile on the percentage scale. A good model will measure the volatility in the data and will project the volatility into the future.

Topics covered:

- Diagnostics
- Autovalidation
- High process variability
- Forecasts
- Pricing
- Modeling Closed Claim Counts

The ultimates for the forecasts are conditional on the previously observed data. There is no need to smooth the ultimates or use Bornhuetter-Ferguson. The ultimates are the true ultimates conditional on the data.

The method of clearing process variance changes is also shown. This is useful when you have 'patterns' found in the hetero which you do not want to project into the future.

The WCom triangle group includes a significant inflation vector based on the known economic inflation in the reporting period. We compare models and forecasts with and without the associated inflation, and show there is no need to adjust for inflation with inflation vectors unless you need to know the inflation after economic inflation. That is, you want to measure social or superimposed inflation.

# 8.2 SDF and more on WCom

SDF is a simulated dataset with a single development factor and constant high volatility. We examine this in PTF and in ELRF. In the course of this we see how high volatility can misdirect judgment about model fit. We forecast with a future accident year and use this to model the Loss Ratios. We see how high volatility in the data leads to high volatility in the loss ratios. The ratio methods in ELRF do not capture the structure of this data, since there is no correlation between incrementals and prior cumulatives. We see how this shows up in the diagnostic plots and forecasts.

Returning to Wcom we look at ways to manually modify a wizard model by introducing constraints. This approach is important in enabling the user to incorporate different ideas about the drivers underlying the data.

# 8.3 Case Study LR High

This video is on assessing the validity of ELRF type models, including the Mack method and illustrating the power of the PTF modelling framework in modelling the paid losses, the Case Reserve Estimates, and the number of claims closed.

We also illustrate how much capital can be released as profit if a less conservative scenario plays out for the next year than that assumed in a conservative forecast scenario.

We begin by analyzing PL(C) in the triangle group LR High using the Mack method in the ELRF modelling framework. Examination of the calendar year residuals reveals a strong negative trend. Trends in the residuals represent the trends in the data minus the trends estimated by the model. This means that for this dataset the Mack method estimates a calendar year trend much larger than the trend in the data.

By including trends and giving zero weight to the early calendar years we design an ELRF model that estimates calendar year trends more in keeping with what is in the data. The resulting mean reserve (as expected) is much lower than that given by the Mack method.

Over estimation of a calendar year trend is illustrated in the PTF modelling framework by simulating a triangle assuming a 10% calendar year trend and setting the trend in the model to be 20%.

Future calendar year trend assumptions can have a major impact on forecast reserve distributions. One of the key differences between the PTF and ELRF modelling frameworks is that in the PTF modelling framework the trend structure and volatility about the trend structure are quantified and the actuary has control on forecast assumptions going forward.

Returning to LR High we look at the identified PTF models for Paid Losses, Case Reserve Estimates (CRE) and the Number of Claims Closed (NCC).

This leads to a discussion of the issues involved in forming a plausible forecasting scenario for the paid losses, incorporating the information from the CRE and NCC models. We also create a forecast scenario to match the Mack method (volume weighted averages) forecasts. The scenario is completely untenable!

Illustration of capital released as profit is also included.

# 8.4 Accident year heteroscedasticity

This video begins with a discussion of accident year hetero and moves on to issues of symmetry in modelling.

First a caveat. If there are significant differences in variance across two or more blocks of accident years it is likely that other trends also differ in these blocks and so the best way to model them is to use subdivided triangles in MPTF.

ICRFS-Plus 10.4 has the capacity to model accident year hetero in just the same way as development year hetero, except that there is no automatic hetero option.

We illustrate the consistency of accident year hetero with development year hetero by modelling a triangle and its transpose.

In triangle group ABC we show how to transpose a triangle so that the development and accident year dimensions are interchanged.

We show that the transposition is preserved if the models are transposed, or indeed if a model such as Statistical Chain Ladder is applied which is symmetric in development and accident directions.

In this case accident year hetero applied to the original triangle corresponds to development year hetero applied to the transposed triangle. We show how to do this and also which tables and graphs enable you to see exactly what hetero has been applied. The forecasts by calendar year are identical for these two transposed cases.

We consider the same situation in the case of link ratio based methods and demonstrate by a simple argument that the forecast values from a volume-weighted average ratio method are identical regardless of whether the ratios are calculated column-wise or row-wise. Hence Mack models predict exactly the same means for the original and the transposed triangle.

The Mack standard deviations however do not share in this symmetry. This fact is explained by the implicit conditioning on the values in the first column in the standard column-wise method. This break in symmetry indicates a flaw in the Mack methodology for computing standard deviations.

# 8.5 Comparing Even and Uneven Triangle Groups

In this video, the difference in data view and forecast output for even and uneven triangle groups is illustrated.