modelling frameworks contained in ICRFS-Plus

The Probabilistic Trend Family (PTF) and the Extended Link Ratio Family (ELRF) modelling frameworks are described in the paper "Best Estimates for Reserves", published in the Proceedings of the CAS, Volume LXXXVII, 2000. The paper is also included in the 2005 Casualty Actuarial Society Syllabus of Examinations.

Probabilistic Trend Family (PTF)

In the PTF modelling framework a model is identified, equivalently, built or designed that captures the variability (volatility) in the incremental loss development array. The variability is described using four components of interest. Trends in the three directions: development period, accident period and calendar period, and the variability of the data about the trend structure. The (process) variability is an integral part of the model.

For more information on the PTF modelling framework click here.

Multiple Probabilistic Trend Family (MPTF)

The MPTF modelling framework is used to design (build) a composite model for multiple incremental loss development arrays. The composite model captures (describes) the variability in each loss development array and the relationships between them. This has applications to modelling multiple lines of business, multiple segments, multiple layers and credibility modelling.

For more information on the MPTF modelling framework click here.

Extended Link Ratio Family (ELRF)

The ELRF modelling framework is an extension of the LRT module where average weighted link ratios are formalized as regression estimators through the origin. The framework provides statistical tests of link ratio methods including Mack and Murphy and many extensions thereof.

Further information on the ELRF modelling framework is available here.

Link Ratio Techniques (LRT)

In this module, standard link ratio methods can be applied to either incremental or cumulative data. Both the ELR method and BF method are also included. Average link ratios can be selected easily, and alternative link ratio methods can be compared either in table format or graphically.

Examples of the Link Ratio Technique module is available here.

Other features in ICRFS-Plus

Predictive Aggregate Loss Distributions (PALD)

Since are no analytical distributions for the aggregate of lognormals, the PALD (Predictive Aggregate Loss Distributions) sub-module simulates from the correlated lognormals in all the cells to obtain distributions of reserves by accident year, calendar year, and the total. The simulated values are used to compute Quantile (Percentile) and Value at Risk (V@R) tables. They can also be used to price Adverse Development Cover (ADC) and other reinsurance programs.

Click here to read further about the PALD module and its applications to PTF based models and MPTF based models.