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

- 2.1 Introduction to the Link Ratio Techniques module and the Extended Link Ratio Family module
- 2.2 ALRT: The Aggregate LRT interface
- 2.3 The Mack method and ELRF
- 2.4 Other models in the ELRF 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

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

## 2. Modelling using the Link Ratio Techniques and Extended Link Ratio Family modules

# 2.1 Introduction to the Link Ratio Techniques module and the Extended Link Ratio Family module (*)

In this video, the Link Ratio Techniques (LRT) module is discussed followed by an introduction to the Extended Link Ratio Family (ELRF) module. Commonly used navigation techniques are also demonstrated as part of the introductory video.

Each tab in the LRT results display is discussed and linked back to the underlying data. Methods of selecting ratio sets are shown. The flexibility in ratio selection is demonstrated; individual ratios can be modified if required.

Introduced in 10.4 are two smoothing algorithms for link ratio methods: two parameter smoothing and three parameter smoothing. Smoothing routines can be applied to a method (eg: volume weighted average) or to a subset of ratios within a method.

Forecast results include:

- A completed triangle table for incremental and cumulative arrays.
- Bornhuetter-Ferguson and Expected Loss Ratio forecasts (a premium vector needs to be associated with the dataset for this output to be meaningful)
- Forecast Summary results including forecasted Calendar period payment stream

The connection from the Link Ratio Techniques (LRT) to the Extended Link Ratio Family (ELRF) is outlined.

- Every link ratio can be treated as the slope of a line or a trend.
- A 'weighted average ratio' can be treated as a 'weighted average trend'.
- The calculation of the weighted average trend can be done using a regression analysis through the origin.
- Regression estimators of trends are equivalent to a weighted average link ratio for the same set of data points.

# 2.2 ALRT: The Aggregate LRT interface (*)

Starting from saved models in LRT, we show how to create a Composite Cumulative dataset and open this in ALRT.

ALRT functions as a frame in which a number of simultaneous instances of LRT can be run. Each instance is under a separate tab and contains a complete LRT interface.

Forecasting in ALRT adds a tab with aggregate tables over all the forecasts. In cases where IL datasets are modelled in one or more of the LRT instances, ALRT checks compatibility of the data types before aggregating the tables. This is illustrated and explained.

# 2.3 The Mack Method and ELRF

In this video we continue with a discussion of the __Mack Method__. The Mack triangle group is used for this discussion as found in the Workbook databases provided with ICRFS-Plus.

The default model in the ELRF modelling framework is Volume-Weighted-Average (Chain Ladder) link ratios formulated as regression estimators through the origin. This method is called the __Mack method__.

Assumptions made by the Mack method include:

- For a given value of X (cumulative development period) the next cumulative development period (Y) lies on the hypothetical 'average trend line', that is average link ratio line.
- Variance assumption: variance of Y (about the average link ratio line) is proportional to X.

Regression estimators through the origin in ELRF are shown to be the same as the equivalent weighted average link ratios in LRT.

The connection between link ratios and regression estimators is reiterated in terms of the ELRF displays. __Residuals are regarded as the difference between the trends in the data and the trends estimated by the method__. The connection between residuals, link ratios, and the data are explained.

It is shown that for the Mack data that the Mack method overfits the large values and underfits the low values. This is indicated by the trend downward in the residuals versus fitted values. The over fitting is a result of that between every two consecutive development years the regression requires a positive intercept.

The __Murphy method__ is an extension of the Mack method with that includes an intercept. From the residuals versus fitted values and the other displays, the Murphy method gives better results than the Mack results.

# 2.4 Other models in the ELRF modelling framework

In the previous video, one extension to the calculation of average link ratios was considered (the addition of an intercept in the regression equations due to Murphy). In this video, this example is returned to in more detail.

The incremental version (Venter) of Murphy's equation is to be preferred as only the incremental value is being predicted since the cumulative component is already known.

If the link ratio-1 in Venter's formulation is not significantly different from zero (ie, the link ratio is 1), then the cumulatives are not predictive of the next column of incrementals. That is, there is no correlation between the incrementals in one development year and the cumulative in the previous development year. In this case, a better way of projecting the incremental in the development period is by taking the average of the incrementals instead of using the previous cumulative.

What happens if there is a trend in the incrementals going down the accident years? It is shown that usually if there is a trend, the inclusion of the trend estimate will have more predictive power than the average link ratios. Note: trends are more helpful for prediction than link ratios. This feature of the data leads us naturally to the formulation of models which incorporate trends directly rather than link ratios - ie the Probabilistic Trend Family!