Fall 2016 #26 (a)

I guess we are assuming "Direct Paid Loss" and "Direct Case and IBNR Loss" are primary gross before commutation. For part (iii), we are not giving reinsurance triangle, but reinsurance gross paid = primary ceded paid. How do we get reinsurance gross case triangle or we don't need it to calculate reinsurance gross ultimate?
Thanks

Comments

  • You have to use the 50% quota-share agreement to calculate the reinsurer's triangles. Before the commutation, you multiply the primary insurer's direct paid and (case+IBNR) triangles by 50% to get the reinsurer's gross paid and (case+IBNR) triangles:

    reinsurer gross paid

    • 2014: 500 1,000
    • 2015: 500

    reinsurer gross (case+IBNR)

    • 2014: 1,000 750
    • 2015: 1,000

    Then to sovle parts (i), (ii), and (iii), you have to figure out how to adjust each cell in the triangles to account for the commutation of year 2014 at the end of 2015. I'm assuming you understand parts (i) and (ii) and just need an explanation for part (iii), reinsurer's gross ultimate loss. The only cells in the above triangles that will change are 2014 at 24 months

    • The 2014 @ 24 mths paid entry of 1,000 is increased by the commutation price of $700 and becomes 1,700.
    • The 2014 @ 24 mths (case+IBNR) entry of 750 decreases to 0. That's the whole point of the commutation - the reinsurer gives the liability back to the primary insurer.

    The reinsurer's triangles after the commutation become:

    reinsurer gross paid

    • 2014: 500 1,700
    • 2015: 500

    reinsurer gross (case+IBNR)

    • 2014: 1,000 0
    • 2015: 1,000

    The final answer for the reinsurer's gross ultimate loss is the sum of these the above 2 triangles:

    • 2014: 1,500 1,700
    • 2015: 1,500
  • Okay, I missed an important information, "reinsurer reserves its portion of the book as the same level of the insurer", so reinsuer gross (case+IBNR) = 0.5 * primary ceded (case+IBNR).
    Thank you!

  • Can someone explain how to get the correct answer for ii from part a? I keep getting

    2014: 1500 3800
    2015: 1500

    To get these numbers I used the net ult reserves before commutation for all ages except the latest and net pd loss after commutation + net reserves before commutation + ceded reserves for the latest age.

    Where net pd losses after commutation is;
    2014: 500 300
    2015: 500

    and net ult reserves before is
    2014: 1500 1750
    2015: 1500

    and ceded reserve is 1750.

    Can you help me understand where I went wrong since the answer key says 2014, 24 is 1800?

  • edited October 2022

    Nevermind, can't figure out how to delete a comment but, I was mixing up the "Net Reserves" = "Net Case & IBNR" and "Net Ultimate Reserves". So instead my net reserves before commutation are as follows;

    2014: 1000 750
    2015: 1000

    Additionally because of the mix up, my ceded reserve was incorrect, it should be 750 instead of 1750 which is the 750*0.5/0.5.

  • Ok, great!

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