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

11. Clusters and MPTF Concepts

12. Capital Management of long tail liabilities

- 12.1 Common drivers and Process Correlation: TG GrossVsNet
- 12.2 Design of a composite model for Company B and allocation of risk capital
- 12.3 VaR, T-VaR, Risk Capital Allocation, and Underwriting risk charge versus Reserve risk charge
- 12.4 Company B LOB ReA versus the aggregate of all LOBs and simulation of a composite dataset from the composite model
- 12.5 Excel based Report for Company B for all LOBs (Company Wide Report)
- 12.6 Introduction, Forecast combinations, and the wizard

14. Other applications of the MPTF modelling framework

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

## 12. Capital Management of long-tail liabilities

# 12.1 Common drivers and Process Correlation: TG GrossVsNet

How do we know if two LOBs have common drivers?

Gross and net of reinsurance data have very much the same trend structure and high process correlation because they have common drivers (especially in the calendar year direction). This is illustrated with a real life example.

However, it is very rare to see two LOBs with similar trend structure or significant process correlation. That is, in general, LOBs do not have common drivers.

# 12.2 Design of a composite model for Company B and allocation of risk capital

A composite model is designed for all the long tail LOBs of Company B. The starting point is the optimal model designed (identified) for each LOB in the (PTF) modelling framework and the associated forecast scenarios.

Clusters are identified based on process correlations between the LOBs.

We find that most LOBs do not have significant process correlation. Moreover, LOBs do not share the same trend structure and process variance. Accordingly they do not have common drivers.

Forecast summaries include:

- Reserve distribution correlations
- Risk capital allocation (percentages) by LOB
- Payment streams by calendar year for each LOB and the aggregate
- Risk capital allocation (percentages) by calendar year for each LOB and the aggregate

Risk Capital allocation by LOB and calendar year is based on a variance/covariance formula.

Calendar year payment streams are critical for the cost of capital calculations. These payment streams are inseparably related to the interaction between of the development period and calendar period parameters. (An accurate projection of the calendar year streams cannot be obtained in any other way).

The volatility of ReA is examined. The process volatility in the past is high. We expect to see the same volatility when we project into the future.

# 12.3 VaR, T-VaR, Risk Capital Allocation, and Underwriting risk charge versus Reserve risk charge (*)

Forecast scenarios going forward are adjusted so that estimates of the means of the reserve distributions correspond to reserves held. For most LOBs they are quite conservative. The CV of the aggregate is smaller than the CVs for most of the individual lines.

Since there is no analytical form for the sum of log normals, we simulate from the projected correlated log normals in each cell for each LOB to find the distribution of aggregates.

Graphs of risk capital allocation for selected VaRs and T-VaRs are discussed.

It is shown that the combined risk charge for reserve and underwriting risk is less than the sum of the individual risk charges.

# 12.4 Company B LOB ReA versus the aggregate of all LOBs and simulation of a composite dataset from the composite model

The LOB ReA has the largest CV and if this were the only line written by Company B it would require a large amount of risk capital. Company B affords substantial risk diversification credit as a result of the reserve distributions exhibiting essentially zero correlation.

A composite dataset is simulated from the composite model for all the long tail LOBs. It is shown to have the same risk characteristics as the real data.

# 12.5 Excel based Report for Company B for all LOBs (Company Wide Report)

A report is generated in Excel for Company B using a report template that exhibits reserve summaries for the aggregate across all LOBs and each LOB by accident year and calendar year. Capital allocation tables and graphs are also given for specific VaR.

One great benefit of an ICRFS-Plus database is that all reports are linked to the corresponding triangle groups and accordingly a report can be found with just a few mouse clicks.

# 12.6 Introduction, Forecast combinations, and the wizard

In this video we discuss various functionality including:

The wizard can now be run on multiple triangle groups in batch mode.

Forecast combinations allow the construction of forecasts consisting of linear combinations of input datasets (including negatives). By way of illustration, we show gross minus deductibles to obtain net forecasts. This technique is useful for analysis of net data where there are negatives as a result of recoveries or subrogations. Similarly for analysising excess layers (2M - 1M = 1Mxs1M for instance).

Forecast settings are now included graphically in the forecast summary window. This important update provides an easy way to compare trends in the model with future forecast assumptions.