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Glad to hear it, thanks for the feedback!

Hi Lori. It depends on the type of actuarial report. If we are are talking about a reserve analysis, I would focus on the following components of the change in the loss reserve estimate: 1) changes in actuarial estimates of ultimate loss between the respective reports, 2) amount of losses paid between reports, and the amount of new exposure added to the portfolio between reports. Any documentation about changes in assumptions is particularly important to review and understand. Ideally, a reader should be able to differentiate between changes in actuarial estimates due to 1) changes in the underlying data, or 2) changes in actuarial assumptions. Hope this helps!

Hello. If you are referring to the chain ladder method, I have a series of videos starting with this one: ruclips.net/video/17ocqFbSw0I/видео.html I call it the loss development method in this video series.

Hello. The gray region represents the period where the reporting date is before the occurrence date. It is not possible to have a claim with those characteristics. For example, suppose a claim has a date of loss (i.e., the accident occurred) on 3/1/2024 and was reported on 2/1/2024. Obviously, a claim cannot be reported before it occurred. Hope this helps!

Hello. Many businesses that purchase claims-made insurance are required to carry a loss reserve liability to recognize the uninsured tail exposure. These businesses typically hire third-party actuaries to estimate their loss reserve need. If you would like more information, feel free to contact me at don.grimm@archeractuarial.com. Thanks!

@@ArcherActuarialConsulting So if I have understood correctly IBNR is basically loss reserve that covers this uninsured tail exposure Maybe I am wrong but I Need help with basics

​@@quratulain5651 IBNR, or "incurred but not reported" can be used in different ways depending on the context. For claims-made coverage, IBNR is sometimes called IBNYR ("incurred but not yet reported"), or "late reported claim reserve". You are correct that an estimate of IBNR is necessary to recognize the uninsured tail liability. Another way to say this is that claims-made coverage does not cover late reported claims (claims reported after the policy effective date); therefore, an additional reserve (i.e., IBNR) is necessary to recognize expected future payments related to late-reported claims.

@@ArcherActuarialConsulting thank you And I must say I am learning a lot from your videos Hopefully I can see more

Hi Favi. IBNR is designed to be an aggregate or "bulk" reserve and, as such, it is not related to a specific claim. That said, there are instances where IBNR is allocated to individual claims. In such instances, it is important to recognize the limitations inherent in the allocation. In practice, the preferred method for establishing reserves for known individual claims is through the case reserving process. If a claims adjuster believes that the case reserve for an individual claim is insufficient, he or she could simply increase the case reserves. IBNR are reserves for both known AND unknown claims. For known (reported) claims, IBNR is an estimate of potential case reserve inadequacies. For unknown (unreported) claims, IBNR is an estimate of the expected loss related to unreported claims (this is also called "pure IBNR"). Hope that helps!

@@ArcherActuarialConsulting Very helpful indeed! Especially the last section.

Hi, thank you for your comment. There are many ways to calculate age-to-age factor averages. It's too strong of a statement to say one way is right or wrong - it really depends on the specific context. I used straight average in this example to keep things simple, but in practice, I tend to prefer a weighted average (all year, 10 year, 5, year etc), or a "double weighted average" (see link below). Another approach that is statistically unbiased is to estimate ATAs by performing a linear regression on historical values. I have a post on LinkedIn that discusses double weighted averages: www.linkedin.com/posts/don-grimm-fcas-maaa-36389597_when-selecting-loss-development-factors-activity-7162796336646467584-tgK4?)

@@ArcherActuarialConsulting Ok, one other thing: Regardless of the method you choose to calculate age-to-age factor averages, this triangle doesn't have enough data? You would take into account accident years before 2016. Correct?

Yes, I would agree that the amount of data in this triangle is insufficient to reliably estimate a loss development pattern. If data prior to 2015 was available, we would want to incorporate it into the analysis (assuming it is representative of the current portfolio). In cases where there is little or no data, or when the available data is volatile, a benchmark pattern is often used. This benchmark pattern can be credibility weighted with the observed data to select a final pattern. This is just the tip of the iceberg of what is a pretty in depth topic. I will consider making a separate video on selecting LDFs in the future.

@@ArcherActuarialConsulting Cool, thanks a lot!

Glad the video helped, thank you!

Hello. Yes, incurred loss development factors are generally designed to be applied to cumulative incurred losses.

@@ArcherActuarialConsulting I have a follow-up question. If incurred losses are not increasing but decreasing from one development year to another that would mean that the incurred losses are not cumulative. Therefore one would have to calculate the cumulative incurred losses before calculating the incurred loss development factors? Is that a correct statement to make? Thank you!

If many or all of your incurred losses are decreasing over time, this is a good sign that you are looking at incremental incurred loss. If the losses are incremental, you must first cumulate them as you suggested. Then you can select LDFs from the resulting cumulative incurred loss development triangle. The key here is to be sure you know the characteristics of the underlying data and avoid making assumptions. It is possible, though relatively rare, for incurred losses to increase over consecutive development periods. A decrease in incurred loss does not guarantee that the incurred losses are incremental.

@@ArcherActuarialConsulting thank you!

Hi. RBNS (reported but not settled) and IBNR (incurred but not reported) are not mutually exclusive concepts, so there can be overlap, depending on how IBNR is defined. Pipeline claims would be considered to be a type of RBNS since the claims have been reported but are not yet settled (paid). Pipeline claims are also a type of IBNR because they have been incurred (the accident has occurred) but not "reported". The word "reported" in IBNR is used in a different sense - here, it is referring to the fact a claim has been incurred but the insurer has not "reported" a corresponding payment or case reserve in its financial statements. This is a tricky topic due to poorly selected and inconsistently applied terminology, IMO. IBNR can be interpreted in a literal way to mean claims that have been incurred but have not yet been reported to the insurer. This type of IBNR is often referred to as "pure IBNR". The more common interpretation of IBNR is more general: it includes pure IBNR as well as expected development on known (reported) claims. I hope this helps! Don

Hi Ethan. Here is one way to go about this calculation. At 4:03 you can see the 1Q 2024 calendar quarter highlighted in yellow. This rectangle has an overall area of 1/4 (1/4 of a year times 100% premium earned). Within this rectangle are two shapes. On the bottom is a triangle representing PY 2024 premium earned in 1Q2024 CQ. This triangle has an area of 1/32 (1/4 of a year times 25% premium earned divided by 2). The area of the triangle makes up 1/8th of the area of the rectangle (1/32 divided by 1/4). Consequently, the remaining portion of the rectangle has an area of 7/8th. We can use the 1/8th and 7/8th as weights to determine a weighted average earned premium for 1Q 2024 CQ. EP for 1Q 2024 CQ = 1/4 x [$1.2M x (1/8) + $1.0M x (7/8)] = $0.25625M. Taking a quick step back - this result says that there is slightly more than $250K of EP in 1Q 2024. Considering that WP is $1M in PY 2023 and $1.2M in PY2024, a result of about $250K per calendar quarter makes sense. It is higher than $250K since a small portion of the $1.2M has earned in 1Q 2024 CQ. Hope this helps!

@@ArcherActuarialConsulting Thank you for taking the time to respond to my question. This totally makes sense now!

@@EthanKornacki Awesome!

Hello. Although this is just sample data that I made up, I would say it is fairly representative of a paid loss triangle for a smaller portfolio. The variability in losses is more a result of the relatively low exposure (and the fact that I made the numbers up!)

Wow Michael, thanks for the vote of confidence, this made my day!

Hi @Noob-qf4yo. The most common triangle structure uses annual evaluations (the columns are evaluated at 12, 24, 36 months, etc) on an accident year basis. The structure may vary based on the data you have available and the goals of your analysis. A reason the "standard" structure is useful is that many industry triangles (and resulting statistics) are available on this basis. This can be useful when trying to compare company data to industry benchmarks. There are an endless variety of combinations of metrics that can be created in a triangle. Think of it this way: any metric that changes over time can be represented in a triangle form. Let me know if you have a question about a specific metric. I like your suggestion about loss trending and put that on my list of future videos. Have a great day! Don

Yep, I got that, but I'm confused about the specific scenarios where we look at accident year losses and in which cases we consider policy year, calendar year, or reporting year.

@Noob-qf4yo I see. It really depends on the circumstance. For loss reserving purposes, losses are generally arranged by accident year. In pricing, losses are often arranged by policy year. For claims-made policies, losses are organized by report year. In all cases, calendar year metrics can be calculated. Calendar year measures reflect the change in AY / PY / RY metrics within a specific calendar year. This video may help: ruclips.net/video/OGvSV2aFV9s/видео.htmlsi=rqq9yw9p8pc4WJCA The best advice I can give you is to attempt understand the difference between the different types and when it arises in a work context, it will make more sense.

Well, that makes sense. Now, another thing is confusing me. Let's consider conducting loss development based on paid losses, leading to ultimate losses. However, I'm confused with the equation ultimate losses = paid + unpaid, where unpaid includes case reserves and IBNR. How does the development on paid losses differ from that on the unpaid portion? Or is it through paid losses that we derive the remaining part of the ultimate loss equation, meaning unpaid losses through ultimate losses developed from paid losses - actual paid losses = IBNR + Case reserves? I'm not sure if I'm heading in the right direction.

Hi @Noob-qf4yo. I think you are heading in the right direction logically. Here are some formulas to summarize your thinking: Estimated unpaid loss = future expected development on paid loss, Estimated unpaid loss = case + estimated IBNR, therefore: Future expected development on paid loss = case + estimated IBNR. Does this help clarify the issue?

@rkm9253 Thank you. I'm open to suggestions on specific topics.

@@ArcherActuarialConsulting How is loss triangle prepared ? What I'd loss development factor

@rkm9253 You may want to take a look at this "how to" video on loss triangles: ruclips.net/video/93DSbXR_l4s/видео.htmlsi=6vAy7joTkxpISpti This video shows how to calculate loss development factors: ruclips.net/video/17ocqFbSw0I/видео.htmlsi=APheWGmKnXu11fNN

Thanks! Yes report year is another common way to organize losses and is mostly used with claims-made related coverages.

@ArcherActuarialConsulting Correct, because it is very important when a claim is reported under the claims-made basis, unlike the occurrence basis.

True

Awesome, thanks!

Thank you for being awesome!

I thought you were going to tell me that you watched the videos to put you to sleep, lol. Thank you for the comment and best of luck with your endeavors! Don

Thank you, I support your decision.

Hello, tail factor selection is a bit of an art and a science. Unfortunately, the techniques are too involved to summarize in a short comment. In practice, actuaries often use the known loss experience (in the form of age-to-age factors) to extrapolate a tail factor using a curve fitting technique or a decay model. Also, it is common for actuaries to select tail factors based on loss experience from similar, but more comprehensive loss data (if it is available). You may find this paper from the Casualty Actuarial Society helpful: www.casact.org/sites/default/files/database/forum_13fforum_02-tail-factors-working-party.pdf

It got me confused quite a bit, but this explanation settles the matter, thanks

What should be 48 months?

@@ArcherActuarialConsulting from 1/1/2020 to 31/12/2023 should be 48 months, right?

@@peterwkf5825You are correct, thank you for pointing out that error!

Greetings!

Hi David, thanks for the feedback! Your understanding is correct except for your assumption that 50% of the ultimate loss for the year will be paid by July 1st. This percentage is determined by the paid loss development pattern (not the portion of the accident year elapsed). One use of a paid loss development pattern is to determine the expected percentage of paid loss a time t, where t is the time elapsed from the beginning of the accident year. Depending on the coverage under review, it may take several years for 50% of payments to be made for a particular accident year. I also have video on loss development patterns here: ruclips.net/video/oN1WlfGiJ-E/видео.html

Hi, that is a good question. The term "incurred loss" is used somewhat inconsistently in the insurance industry. In most contexts, "incurred loss" refers to paid loss + case reserves (this is sometimes called "case incurred"). However, "incurred loss" is less frequently used to refer to paid loss + case reserves + IBNR. When it is used in this latter sense, it sometimes is called "bulk incurred". Because of this ambiguity, it is always good to look for clues in your data to deduce how the terms are being used in a specific context.

Thank you!

Hello and thanks for the question. The loss experience for an accident year is defined by the date of loss of the underlying claims. The green triangle in this video from 1/1/24 to 1/1/25 represents policies written in 2024 which are exposed to loss in the same year. Being exposed to loss means that the policies are exposed to accidents. As you correctly point out, a portion of the policies written in 2023 are exposed to loss (accidents) in 2024. So, accident year 2024 is composed of losses (accidents) related to policies written in 2023 and 2024. The point being made in this video is that an accident year is generally composed of losses from more than one policy year. In the AY vs CY video, the triangle is already organized by accident year, so the interpretation is straightforward. In this video, I'm showing how an AY is made of losses stemming from multiple policy years. Hope this helps!

Thanks that’s helpful. I suppose I am still confused between AY and CY then. In this video, AY for loss = CY for earned premium, whereas in the other AY vs CY video, AY and CY have different definitions. If AY already includes prior year, then does CY just add on further PYD? In this diagram however, it assumes that all 1 year policies have run off and so AY = CY?

Hi. I went back and watched my video. I think the source of confusion may be from my statement that "an accident year is another name for a calendar year, but specifically for loss". This was a poor choice of words. The important takeaway is that accident year losses are on the same *basis* as calendar year earned premium. The shared basis is exposure to loss. - For premium, exposure to loss corresponds to the earning of premium during a calendar period. - For loss, exposure to loss corresponds to losses occurring during an accident period. So, one can compare AY losses to CY earned premium (say, as a ratio) and know there is a consistent exposure basis.

Hi Emily. I am not familiar with the latter method, but they sound like they may be the same.

Hi Emily. A loss development pattern can be represented in a few ways: 1) as % of ultimate 2) as incremental LDFs (loss development factors) 3) as cumulative LDFs Here are the relationships between the above: - Cumulative LDFs are a multiplicative cumulation of incremental LDFs - The % of ultimate is the reciprocal of the cumulative LDFs. Assuming you have a paid loss development pattern of cumulative LDFs, you can calculated the expected % paid at each age by taking the reciprocal of the corresponding cumulative LDF. Below is an example for a single maturity: Cumulative Paid LDF @ age 12 = 2.00 Exp % Paid @ age 12 = 1 / 2.00 = 50% Hope this helps!

Thanks for the suggestion Emily. I do plan to make one some day. In the meantime, let me just say that the paid loss development method and the incurred loss development method are nearly identical except that paid losses are used in the former and incurred losses in the latter.

Thank you!

Thanks for the feedback!

Thank you!