Category: Terms

Cumulative claim development factors (a.k.a. age-to-ultimate factors and claim development factors to ultimate) are calculated by successive multiplications beginning with the tail factor and the oldest age-to-age factor and projects the total growth over the remaining valuations.

Cumulative CDFs are often greatest for the most recent AYs and the smallest for the oldest accident years.

Actuaries refer to the most recent, less-developed AYs as immature and the oldest, most-developed AYs as mature.

Calculating CDFs

Using the selected age-to-age factors from earlier exercises, calculate the following:

• Selected tail/ultimate factor = 1.00
• CDF at 4 years= (selected tail factor) x (selected development factor 4-5 years) = 1.00 x 1.125= 1.125
• CDF at 3 years= (selected tail factor) x (selected development factor 4-5 years) x (selected development factor 3-4 years)
  = (CDF at 4 years) x (selected development factor 3-4 years) = 1.127 x 1.125 = 1.267
• Continue in this manner until computing the Reported CDF at 1 year
• = (CDF at 2 years) x (selected development factor 1-2 years) = 2.437

Try some of the calculation in the below exercise and see that if you have got it right!

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It contains the terms those are important to understand what exactly the reserves meant and which would make your life easy for the upcoming exercise.

In case you are confident enough that you can leave them, feel free to ignore them completely 🙂

Somehow, Short-tailed and long-tailed suggest only if the claims are reported and settled quickly or are delayed. But these are used everywhere in General Insurance.

Short and Long tailed is an important concept there is not an exercise in which we are not going to use it, consider pricing, reserving or even Asset Liability Management.

Short Tailed

Short tailed means that the claims are generally reported quickly and settled quickly by the insurer.

Long Tailed

Long tailed means that there is a sizeable proportion of total claim payments that takes a long time to be reported and/or a long time for the insurer to settle.

Loss development factors (a.k.a. LDFs or age-to-age factors and claim development factors ) are calculated by successive multiplications beginning with the tail factor and the oldest age-to-age factor and projects the total growth over the remaining valuations.

Loss development factors are significantly relied upon in many actuarial loss reserving methodologies. They can be calculated entirely from loss triangle data– no additional data needs to be provided to the actuary to calculate loss development factors. A loss development factor is the loss value in a loss triangle divided by the value immediately before it in the loss triangle.

To choose which development factor to use for projecting claims for future years, any of the following can be considered

• average of all the development factors can be taken or
• as a conservative measure, the largest development factor for any development year can be taken or
• weighted average can be taken.

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Points to note in LDFs

You probably notice a few interesting things with this triangle in the exercise. First off, it is smaller than the loss triangle. There is one fewer row and one fewer column. Remember, an LDF is calculated from two numbers, so there is no loss development factor available for 2014 where there is only one loss observation. Also, there are only 6 loss development factors that can be calculated for the 2008 year.

The next point of interest to most people is that all of the factors are over 1. This isn’t a surprise as paid losses will generally be higher in each passing year as more and more losses get paid. For accident years that are very old and have no claim activity, the loss development factors will drop to 1.000 meaning that losses are unchanged between successive valuations

Incurred claims

Incurred Claims is an estimate of the amount of outstanding liabilities for a policy over a given valuation period. It includes all paid claims during the period plus a reasonable estimate of unpaid liabilities. It is calculated by adding paid claims and unpaid claims minus the estimate of unpaid claims at the end of the prior valuation period.

Components

Benefits paid during the reporting period and Change in Outstanding reserves during the period

Calculation

Benefits paid during the reporting period + (Total reserves at the end of the reporting period – Total reserves at the beginning of the reporting period)

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Related Questions

Loss ratio is the ratio of claims incurred by the insurance company to amount of premiums earned by it.

Loss Ratio

Loss ratio is the ratio that you will find in almost all the sheets and is the most amazing way to quantify the profitability.

If someone said to you that the LR is 180%, it means that the LR is completely yikes and the company should close the business, but consider this that the company has LR of 20% (in another business, of almost same EP) and this satisfies the LR to 100%.

Loss Ratio = Claims Incurred for the year (ultimate losses for the company)/ Earned Premium for the year

We have already explained both of these components in our earlier exercise. You will generally see a LR of 75% – 92%. In India, the TP loss ration mostly remains above 100% for most of the companies, and it is one of the mandatory offering by the regulator i.e. IRDAI

In simple language, a high loss ratio is an indicator of financial distress and indicates that for each dollar of premium earned, the company is shelling a high sum of money as claims paid to policyholders.

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Questions Related to Loss Ratio

Earned Premium is important to the company and is of utmost use while calculation of Reserves

Earned Premium

Earned premium is the premium collected by an insurance company for the portion of a policy that has expired. In other words, the earned premium is what the insured party has paid for a portion of time in which the insurance policy was in effect, but has since expired.

Earned Premium (EP) is that portion of a policy’s premium that applies to the expired portion of the policy. Although insurance premiums are often paid in advance, insurers typically “earn” the premium at an even rate throughout the policy term. The unearned portion of the premium that has been paid is kept in the “unearned premium reserve.”

There are different types of methods from which Earned premium is calculated. The most common is 1/365 method while the others maybe 1/24, 1/8 or can be customized according to the policy but should be reasonable else as an actuary, you are answerable to all the regulator and auditors’ queries and this could be one.

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Questions Related to Earned Premium

EP is calculated hereby using 1/365 method.

Other Reserves

Insurers may also hold catastrophe reserves or other claims equalisation reserves.

Catastrophe Reserves

Catastrophe Reserves — reserves on a captive’s balance sheet that are for paying neither known nor incurred but not reported (IBNR) losses. The ideal would be to build up these catastrophe reserves for the rainy day when they will be needed.

We are not learning how to calculate Cat Reserves here. The definitions are for knowledge purpose and you should be aware of all the reserves that you may come across later.

Claim Equalisation Reserves

Pending

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Questions Related to Other Reserves in a GI company

Outstanding Claim Reserves Definition

Outstanding claim reserves provision for the estimated amount of claims that have not been settled. It can be interpreted to include only claims that have been reported, or to include all claims not yet settled.

These are cash reserves held by insurance companies to cover unpaid claims

This is a set aside amount for insurance benefits that have already been claimed by the policyholders but have not been settled yet. It can be said a reserve for Incurred/Reported but not settled liabilities.

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Questions Related to Outstanding Reserves