Envision from Triangles

When only Triangle data is available

ReservePrism facilitates the development of methodologies other than the customary triangle methodologies. However, in some situations, only loss development triangle data is available. In this case, ReservePrism has an Advanced Triangle Engine that back-fits the simulation parameters from your Paid, Incurred, Closed Count, and Reported Count, etc, triangles. Triangle data has important information "squeezed" (accumulated) away, thus the parameter fitting is not as accurate as it would be if detailed claim data were directly fitted. However results are very promising due to preliminary tests of our optimization algorithm.

Knowledge Base: What is Average Absolute Incremental Error (AAIE)?
Knowledge Base: What is Payment Count Triangle?

Example 1, Frequency and Report Lag Fit through Reported Count Triangle.

  • Assume starting parameters for the Report Lag Distribution X
  • Form a simulated Reported Count triangle S  
  • Do a Maximum-Likelihood Fit between S and your real Reported Count triangle R, by minimizing the Average Absolute Incremental Error. System concludes with the best fitted Report Lag parameters of X.
Report Count Triangle

Let us assume the triangle on the left is your company incremental Reported Count Triangle.


You don't know your report lag distribution or you only have a rough estimate of the mean report lag value from your claim department.


Let us find out.


Report Count Triangle

First, let us load the triangle to ReservePrism.

Report Lag Prove

You only need to select a distribution family. ReservePrism then optimizes the report lag fitting by minimizing the Average Absolute Incremental Percentage Error between the fitted and the real Report Count Triangles.


After the fitting calculation, your coverage's Annual Frequency is generated as well.

Report Lag Prove

The triangle on the left is the simulated Report Count Triangle, generated from the fitted Report Lag distribution.


Your Report Lag distribution is: Exponential (rate=0.009247)


Example 2, Settlement Lag Fit

Similar to the Report Lag distribution calculation, ReservePrism finds your Settlement Lag in the following steps. But this procedure is much more complex, and involves both of your Reported Count and Closed Count triangles as input.

  • Assume starting parameters for the Settlement Lag Distribution X
  • Form a simulated Closed Count triangle S  
  • Do a Maximum-Likelihood Fit between S and your real Closed Count triangle R, by minimizing the Average Absolute Incremental Error. System concludes with the best fitted Settlement Lag parameters of X.

Example 3, Loss Size Severity Fit

Back-fitting Severity from Paid Loss and Count triangles is very challenging due to its nature of information loss. But we applied these methodologies in ReservePrism.

Tweedie Compound Model

We are in the process of finalizing this Tweedie-Weibull model from published CAS papers combined with our own modeling methodologies.

Paid Loss Brute Force Fit Model
  • Assume starting parameters for the Severity (Loss Size) Distribution X
  • Based on the count values from your real Payment Count triangle (or simply Closed With Payment Count), sample X from each triangle cell
  • De-Trend each triangle cell
  • Applying Limit and Deductible, applying P0, applying Trend and Alpha, and possible, applying Copula, from those samples in each cell
  • Form a simulated Paid Loss triangle S
  • Do a Maximum-Likelihood Fit between S and your real Paid Loss triangle R, by minimizing the Average Absolute Incremental Error. System concludes with the best fitted Severity parameters of X.