TAC Actuarial Learning

Author: Mayank Goyal FIA

  • Run Off Triangles in GI

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    The run off triangles helps in forecasting the reserve amount that needs to be held by the insurer at any point in time so that they have sufficient assets to cover their liabilities at any point in time. They can be used to forecast the different types of reserves.

    What are run off triangles?

    Run off triangles are a method used to model claims experience. They’re specifically used to estimate the future claims that will be reported based on those already reported. When a claim event occurs there will be some time before it is reported or notified to the insurer – this is known as a claim delay.

    How run off triangles is prepared for calculating reserves?

    Generally, one axis of the run off triangles 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. Development year specifies after how many years of the claim reported it is getting settled.

    The upper-left-side run off triangle is usually formed with paid claim amounts (sometimes with incurred claim amounts). The lower-right-side triangle is a projection of future claim payments.

    However, it is not always the case. The run-off triangles can also be based on the Reporting year or Underwriting year. But in general, what we use is Accident year.

    Where are run off triangles used in reserving?

    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.

    When a claim event occurs there will be some time before it is reported or notified to the insurer – this is known as a claim delay. The insurer will incur numerous claims in a calendar year, and each of those claims will have a claim delay.

    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.

    They look like the example below and can have 100 of quarters, the older the company, bigger the triangle.

  • Actuarial GI Reserving Introduction

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    Actuarial GI Reserving is standard practice in General Insurance companies.

    Below are the questions which you may have. As this is just an introduction to Reserving, we are not going to cover any concept but just questions that would be discussed in detail in the upcoming exercises.

    What is Actuarial Reserving in General Insurance?

    In General Insurance Industry, whenever a claim is reported, it takes sometime before the claim is fully paid (or runoff) by the insurer because of a number of reasons.

    So it is very important for the company to keep the reserve of money in anticipation of such claims that will need to be paid in the future.

    In Liability LOB, the delay could be in years.

    What are the reasons that claims may be delayed?

    Few of them would be:
    – delay in claim notification, 
    – delay in claim notification and payment due to bureaucratic  reasons,
    – claim payment withheld until the final payment amount is decided by a loss assessor in a motor accident,
    – small amounts and a large number of claims by individuals received at different times after a catastrophic event has happened in an area that has damaged the property or might be because the insured is suing the insurer in the court for the final settlement amount to be paid.

    Why the actuarial reserves like IBNR, OS are created?

    An insurer may not know the exact figure for total claims in a year but it has to estimate that number with the highest level of accuracy possible.
    The insurer must reserve a certain amount for the liabilities that are incurred but not reported as in the above events or for those which are reported but are yet to be paid.

    What are the types of reserves in General Insurance?

    Incurred But Not Reported – IBNR
    Incurred but not enough Reported – IBNER
    Outstanding Reported Claims Reserves – OS Reserves
    Catastrophe Reserves – Cat Reserves

    We will learn more in the later chapters.

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  • Actuarial GI Reserving Tutorial

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    Actuarial GI Reserving is a standard practice in General Insurance companies across the world.

    By learning Reserving, it becomes easier for you to understand the concepts behind the Reserve liabilities of a GI company. TAC Learn makes it easy for you to understand these Reserving concepts using our Actuarial GI Reserving tutorials.

    The content and exercises provided are generalized to be understandable to freshers/ intermediates and not expert level exercises. Many of the extreme content like smoothening, pattern basis, trendsetting, market competencies, tail factors have been completely or partly ignored for keeping it simple and short.

    Examples in Every Chapter

    This Actuarial Reserving tutorial and all the upcoming tutorials contain many Reserving exercises based on an example related to that exercise. This helps you to see and understand the exercise in a much better way and further you can try it in your personal excel.

    Using Microsoft 365 and embedding the sheets, you can edit the excel, and the results will change accordingly.

    Try editing the numbers below in order to understand how are we going to perform our future exercises

  • IBNR

    Incurred But Not Reported or IBNR reserves are a part of claims reserves estimated by insurers for reporting on their financial statements. Claims reserves are estimates of claims that have occurred on or before the financial statement report date but which have yet to be paid. This a current liability that has to be reported regularly on the insurer’s financial statements even though the actual final settlement cost of the claims may be unknown to the entity at that date. Accuracy of these claims reserves estimates is important to the insurer for a number of reasons. It impacts the insurers:

    1. Profitability, financial position, and strength which influences how investors and regulators view
    2. Pricing, underwriting, strategic and financial decisions made by its management

    Inaccurate estimates will project an incorrect view of the insurer’s health and may result in investors and regulators taking actions that may be detrimental to the company. The insurer’s own management may take incorrect and possibly adverse action to correct perceived failings or benefit from perceived wellness that erroneous estimates convey.

    Incurred But Not reported IBNR Reserves
    Introduction of Incurred But Not Reported (IBNR Reserves)

    Claims reserves comprise of two main portions:

    1. Outstanding case reserves for claims incurred and reported as of the financial report date
    2. Incurred but not reported (IBNR) claims reserve estimate, as mentioned above, which consists of:
      • A pure IBNR reserve estimate, that is claims that have incurred but which has not yet been reported to the insurer
      • Provision for future development of claims already reported to the insurer
      • Provision for claims that will be reopened in the future
      • Provision for claims that have been reported but which are not yet recorded in the insurers books

    Outstanding case reserves are determined by insurer’s claims department or an independent claims adjuster hired by the insurer while the Incurred But Not Reported or IBNR reserves estimate is usually determined / advised by an actuary. The focus of this post is on the latter estimate.

    A non-life insurer is required to hold a liability for the unexpired risk that is valued at not less than the sum of unearned premium reserve and the premium deficiency reserve, where the:

    • Unearned premium reserve (UPR) is the unexpired portion of the premium which relates to business in force at the balance sheet date; and
    • Premium deficiency reserve (PDR) is the amount if any by which the expected settlement cost, including settlement expenses but after deduction of expected reinsurance recoveries, of claims expected to be incurred after the balance sheet date in respect of policies in force at the balance sheet date, exceeds the unearned premium reserve.

    We will soon cover the process for all the Methods of Reserving using Run off triangle and stochastic modelling with description on each of them.