# What is a run-off triangle?

## 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 development of run-off triangles is generally used for estimating incurred but not reported claims for insurance portfolios, in order to set appropriate reserves that are in compliance with regulatory requirements as well as the company’s risk appetite. Also known as: Development Triangle or Run-off triangle.

What is a loss triangle in insurance?

Loss Triangle — a table of loss experience showing total losses for a certain period at various, regular valuation dates, reflecting the change in amounts as claims mature. Older periods in the table will have one more entry than the next youngest period, leading to the triangle shape of the data in the table.

### How do insurance triangles work?

A loss triangle is the primary method in which actuaries organize claim data that will be used in an actuarial analysis. This loss triangle totals paid loss data in each of two categories. The first is accident year. Simply put, all paid losses from all claims occurring in the accident year are totaled.

How do you calculate loss ratio?

The loss ratio is calculated by dividing the total incurred losses by the total collected insurance premiums. The lower the ratio, the more profitable the insurance company, and vice versa.

How do you calculate expected loss ratio?

How to Calculate Expected Loss Ratio – ELR Method. To calculate the expected loss ratio method multiply earned premiums by the expected loss ratio and then subtract paid losses.

## What is development triangle?

A development triangle is a table that shows changes in the value of various cohorts over time. Development for any of these cohorts (for example, accident year claims) is the change in the value for the cohort over time.

How do you calculate cost loss?

Losses in loss ratios include paid insurance claims and adjustment expenses. The loss ratio formula is insurance claims paid plus adjustment expenses divided by total earned premiums. For example, if a company pays \$80 in claims for every \$160 in collected premiums, the loss ratio would be 50%.

What is a pure loss ratio?

Pure loss ratio is computed by dividing total losses by total premium. As an example, if you are paying a \$1,000 annual premium and have claims of \$100, you divide \$100 by \$1,000 which produces a pure loss ratio of 10%, which is an excellent result for the insurance carrier.

### What is a profitable loss ratio?

How to run off triangle of Claims data?

Run off triangle of accumulated general insurance claims data. GenInsLong provides the same data in a ‘long’ format. A matrix with 10 accident years and 10 development years. TAYLOR, G.C. and ASHE, F.R. (1983) Second Moments of Estimates of Outstanding Claims.

How does the loss triangle work in insurance?

This loss triangle totals paid loss data in each of two categories. The first is accident year. Simply put, all paid losses from all claims occurring in the accident year are totaled. Now keep in mind, these losses are cumulative, not incremental. This means loss payments are included regardless of when the payment was made.

## What is the role of run off triangles in actuarial?

Reserve calculation is necessary for the long-tailed claims (eg: motor claims) which takes many years to get settled. One axis of the run-off triangle matrix (vertical one) denotes accident year and the other axis (horizontal one) denotes development year (or, delay year). Accident year specifies in which year the claim is reported.

What is the loss triangle in HB actuarial?

The easiest loss triangle to explain is the accident year paid loss triangle. This loss triangle totals paid loss data in each of two categories. The first is accident year. Simply put, all paid losses from all claims occurring in the accident year are totaled. Now keep in mind, these losses are cumulative, not incremental.