Multiple Probabilistic Trend Family (MPTF)
The MPTF modeling framework is used to design (build) an optimal composite model for multiple incremental loss development arrays. The identified composite model captures (describes) the variability in each loss development array (a la PTF) and the relationships between them.
This has applications to modeling multiple lines of business, multiple segments, multiple layers and credibility modeling.
Relationships between lines of business, for example, involve two types of correlations; process correlation and parameter correlation.
Clusters of lines of business can also be designed where correlations between any two lines of business in different clusters are zero.
To view a demonstration video on Capital Management of all long tail liabilities click here.
An optimal composite model forecasts lognormal distributions for each cell in each loss development array (in the composite dataset) including the correlations within cells in an array and cells between arrays. These induce correlations between arrays for each pair of accident years, calendar years and aggregates.
For more information on optimal reinsurance calculations see the section on the PALD (Predictive Aggregate Loss Distribution) module.
Benefits and Advantages
The MPTF modeling framework is an extension of the PTF modeling framework so all the advantages of PTF apply. There are numerous other benefits afforded by the paradigm shift. Here are some:
- A company wide picture of multiple lines can be created in one composite model that includes the volatility in each LOB and their inter-relationships.
- Capital can be allocated to each line optimally using covariance formulae driven by the data (business)
- Diversification afforded by way of merger and/or acquisition.
- A composite model can be constructed for different layers and used to design both optimal outward and inward reinsurance including that of excess layers.
- Credibility modeling for a 'small' triangles or triangles with much process variability.