1. Introduction to ELRF™

1.1 Introduction to ELRF™ database structures

The database functionality and navigation is studied. Data, models and links to reports all reside in one relational database. A database can either be remote (on a server that is shareable) or local. Communication between two databases has the same intuitive feel as using Windows Explorer for communicating between two sub-folders. The objects in the database are Triangle Groups (TG) and Composite Triangle Groups (CTG). TGs (and CTGs) also contain objects, namely, triangles, exposures, premiums, data sets, models and links to reports.

This video demonstrates:

• database manipulation
• database structure
• triangle group structure
• using variables and values to filter triangle groups
• system navigation
• creation of new databases and communication between two databases
• new triangle types

1.2 Overview of ELRF™ modeling frameworks

In this video, a brief overview of the modeling frameworks included in ICRFS™ is presented.

These frameworks include:

• Link Ratio Techniques (LRT) including Bornhuetter-Ferguson
• Extended Link Ratio Family (ELRF) as discussed in the paper "Best Estimate for Reserves"
• Probabilistic Trend Family (PTF) modeling framework
• Multiple Probabilistic Trend Family (MPTF) modeling framework

There is a paradigm shift between link ratio techniques (LRT) and the probabilistic modeling frameworks PTF and MPTF. The ELRF modeling framework provides the bridge between the two frameworks.

An identified model in the PTF modeling framework gives a succinct description of the volatility in the data. The description of the volatility is represented by four graphs, which tell a story about the data.

Benefits of the ICRFS™ software package include:

• A user configured, easily navigated database
• The database is a repository for the data, models, and forecast scenarios
• Uneven sampling periods: for example, Accident year reserves versus quarterly evaluations.
• Models are saved in the triangle groups
• Monitoring and updating every review period is a seamless operation
• Diagnostics for existing link ratio methods
• Pricing both retrospective and prospective reinsurance structures
• Pricing for different limits for different years
• Future accident (underwriting) period segmentation pricing
• Understandable probabilistic models summarised by four interrelated pictures.
• Correlations (all three types: process, parameter, and reserve) and trends are measured from the data.
• Economic Capital: risk charges for combined reserve and underwriting risks. (Note there is usually additional diversification credit obtained for the combined risk charge on reserves and underwriting).
• modeling wizard
• Reinsurance evaluation

modeling multiple triangles simultaneously in the MPTF module has additional applications and benefits including risk diversification analysis, capital allocation analysis, credibility modeling, and many other applications as seen in subsequent chapters.

1.3 Uncertainty and Variability

Variability and uncertainty are two distinct concepts and cannot be used interchangeably. Variability is an observed phenomenon that is to be measured and where appropriate explained. Uncertainty, on the other hand, refers to knowledge about variability.

This is easiest to explain by way of example. We demonstrate by comparing two games of chance where the parameters of the games are known. In this case, we have no uncertainty in our knowledge about either game. We 'know' the mean, standard deviation, and indeed the probabilities of all the outcomes.

Parameter uncertainty leads to uncertainty in the variability of the process- our knowledge about the variability is uncertain. The inherent variability (process variance) cannot be reduced.

1.4 Manual creation of Triangle Groups

In this video, manual creation of a triangle group is illustrated. Although triangle groups are usually created via an importing macro, it can be useful to create triangle groups and triangle manually for small projects.

Creating triangle types and triangles are also demonstrated along with transferring data and models between similarly sized triangle groups.

2. modeling 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.

Two smoothing algorithms for link ratio methods are available: 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™.

The default model in the ELRF modeling 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 modeling 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!