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## What is a run off triangle?

Run-off triangles (or delay triangles) are two-dimensional matrices that are generated by accumulating claim data over a period of time. The claim data is run through a stochastic process to create the run-off matrices after allowing for many degrees of freedom. Run-off triangle.

### What is run off triangle and why is it used?

The run off triangles are used to estimate how much or how many claims have been incurred in a reporting period (eg financial year) but are not yet reported and a reserve is held for this. It’s called an IBNR – incurred but not reported reserve.

#### How do insurance triangles work?

An insurance claims triangle is a way of reporting claims as they developer over a period of time. It is quite typical that claims get registered in a particular year and the payments are paid out over several years. So it becomes important to know how claims are distributed and paid out.

What are reserving triangles?

The idea behind most reserving techniques – that of compacting historical loss experience into a loss development triangle, and using these triangles to project the total claims amount to ultimate for every accident period (what one may call the “triangle trick”) – has proved to be a powerful tool for underwriters and …

How is IBNR reserve calculated?

With an estimate of the total incurred claim cost, then the calculation of IBNR is as straightforward as subtracting the claims already reported from the total incurred claim costs, as shown in Figure 1.

## How do you calculate average cost per claim?

The average cost per claim is calculated by dividing the number of claims filed in a particular year by the total cost that has been incurred to date.

### How do you calculate loss development factor?

A loss development factor is the loss value in a loss triangle divided by the value immediately before it in the loss triangle. For example in the loss triangle example, the first loss development factor for accident year 2008 is equal to \$688,542 divided by \$403,082 (the value right before it).

#### What is the main purpose for claims development triangles?

Claim triangles and their limitations Triangulation methods work by banding homogeneous groups of claims together into either accident, underwriting or reporting period cohorts, and then observing the development patterns. The analyst observes the historical patterns and uses them to predict future development.

Why is loss reserving important?

A loss reserve is an accounting entry that estimates the amount an insurance company would have to pay out on future insurance claims on policies that it has underwritten. Estimating the correct loss reserve is important for an insurance company as it directly impacts profitability and solvency.

Does Case Reserve include IBNR?

Case reserves are computed as the difference between the incurred losses (not shown in Figure 1) and the paid losses. Therefore IBNR includes development on known claims as well as a provision for claims that have occurred but not been reported as of the evaluation date.