Applying reinsurance partway through an year

Discussion in 'SP7' started by abcd1234, Nov 27, 2016.

  1. abcd1234

    abcd1234 Member

    Suppose I write business evenly throughout the 2011 underwriting year which runs from 1st January to 31st December.
    Suppose this business earns evenly over the course of two years (i.e. annual policies) - i.e. all the premium is earned in 2011 and 2012 for the 2011 underwriting year.

    Now suppose I have some quota share reinsurance (e.g. 72% recoveries) then which applies from 1st October 2011 on an underwriting year basis.

    How do I calculate how much recovery I am expected to make for each of the 2011 and 2012 earned years, in respect of the 2011 underwriting year?


    My thinking was that if business is written evenly throughout the year, then only 3/12 of the total business written in 2011 can be recovered (as 3/12 of the 2011 business is assumed to be written during 1 Oct 2011 to 31 Dec 2011).
    But how would this be split across the 2011 and 2012 earned years (assuming a uniform earning pattern)?
    Would it be that 1.5/12 of the business written from 1 Oct 2011 to 31 Dec 2011 would be earned in 2011 (assuming annual policies) and 10.5/12 would be earned in 2012?
    This would mean:
    - for the 2011 underwriting year, 3/12 x 0.72 of the gross amount would be recoverable in the whole 2011 underwriting year
    - for the 2011 earned year in respect of the 2011 underwriting year only (not 2010 u/w year), 1.5/12 x 3/12 x 0.72 of the gross amount would be recoverable in this whole 2011 earned year
    - for the 2012 earned year in respect of the 2011 underwriting year only (not 2012 u/w year), 10.5/12 x 3/12 x 0.72 of the gross amount would be recoverable in this whole 2012 earned year

    Am I correct or if not please let me know.
     
  2. Hemant Rupani

    Hemant Rupani Senior Member

    I agree with you if you meant gross amount by ultimate loss amount for policies written in 2011. Inflation ignored.
     
  3. abcd1234

    abcd1234 Member

    Yep ignoring inflation. The gross amount would be the gross ultimate IBNR in this case.
    Thanks!
     
  4. Darren Michaels

    Darren Michaels ActEd Tutor Staff Member

    Hi there

    To be honest I think you are confusing some concepts here. "Earned year" is not a well used/recognised term.

    When were are talking about earned and unearned, we normally talk about exposures, so the most logical/common amount to talk about earning is the premium. Also, you need to refer to a point in time so that you can say what the earned premium or unearned premium is at that time.

    So taking your example, lets suppose we write £400 of premium in 2011.

    With the three standard assumptions (annual policies, risk uniform over policy period, policies incept uniformly over year) this means at 31.12.11 £200 would be earned and £200 unearned. The latter would be earned during the course of 2012.

    All of this is gross of reinsurance so far.

    Now lets suppose we have this 72% QS applying from 1 October 2011 onwards. When you say it applies on an underwriting year basis, I assume you mean a risks attaching basis. In other words, it applies to underlying policies that are written during the period of its operation.

    Now, £100 of premium will be written in the last quarter of the year (where the QS applies) and on average this incepts midway through the quarter, so it will be 1/8 earned by the end of the year. Hence the gross earned part of this premium is £12.50 at 31 December and then net earned premium will be 28% of this ie £3.50.

    You also have the £300 of written premium in the first 9 months of the year, of which £187.50 is earned by the end of the year. In reality there may have been a QS reinsurance in the previous year which would protect this business as well.
     

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