1 / 12

Math 479 / 568 Casualty Actuarial Mathematics

Math 479 / 568 Casualty Actuarial Mathematics. Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 13: Reinsurance II – Exposure Rating and Increased Limits Factors October 14, 2014. Reinsurance Pricing. Pro rata reinsurance

raymond-hernandez
Download Presentation

Math 479 / 568 Casualty Actuarial Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 13: Reinsurance II – Exposure Rating and Increased Limits Factors October 14, 2014

  2. Reinsurance Pricing • Pro rata reinsurance • Straightforward pricing, since a percentage • Consider adequacy of primary pricing • Excess reinsurance • Price is generally specified as a percentage of “subject premium” • Two traditional approaches to pricing: • Experience rating • Exposure rating

  3. Exposure Rating • Allocation of primary premium to different “layers” of coverage • Consider adequacy of primary premium • Depends upon: • Attachment point and limit of reinsurance layer • Primary premiums at different policy limits • Increased limits factors (ILFs)

  4. ILFs • Consider a loss severity (size per claim) distribution • For example: exponential distribution:

  5. ILFs (cont.) • Specifically, consider an exponential distribution with a mean of 20:

  6. ILFs (cont.) • Suppose that the primary insurer writes a “basic limits” policy, with a limit of 25 per occurrence • Notation (Y = insurer’s payment):

  7. ILFs (cont.) • One item of interest: • Another item: what is the expected size of a claim paid by the insurer?

  8. ILFs (cont.) • Consider different policy limits written by the primary insurance company: Policy LimitE[Y]“ILF” 25 14.27 1.000 50 18.36 1.287 100 19.87 1.392 Unlimited 20.00 1.402

  9. Exposure Rating • Suppose basic limits (BL) premium = $100. Policy LimitPremium 25 (BL) 100.00 50 128.70 100 139.20 Unlimited 140.20

  10. Exposure Rating (cont.) • Consider 50 x/s 50 layer: • Worth 139.20 - 128.70 = 10.50 • But this value can also be determined via ILFs: 100 (1.392-1.287) = 10.50 • Exposure rating involves using quantitative relationships between limits to allocate premium to different layers

  11. Examples • What proportion of the primary premium on a 100 limit policy should go to the 50 x/s 50 reinsurance layer? • Suppose you determined that primary premiums are, in general, 10% inadequate. What proportion of the 50 limit policy premium should go to the 25 x/s 25 layer?

  12. Caveat • A big issue here is the nature of the ILFs. • How are expenses handled? • How is risk load handled? • A reinsurer might want to use loss-only ILFs, without risk load, to determine the loss portion of the layer, then determine the final reinsurance premium by incorporating its own expenses and risk load. • Thus, adjustments may need to be made to results associated with situations like the examples.

More Related