1. 1 Math 479/568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 12: Reinsurance I October 9, 2014

2. 2 Agenda Reinsurance I –Basic concept –Who ’ s responsible for the loss? –Purposes and functions –Types –Issues

3. 3 Reinsurance – the Basic Concept “ Reinsurance ” is essentially the “ insurance of insurance ” –One insurer “ shares ” its business with another –Both the premiums and losses are shared –Sharing can occur as a percentage, or based on a size-interval of loss Reinsured

4. 4 The Basic Concept (cont.) Framework: –Insurer sells an insurance policy to the insured –Insurer (possibly) purchases reinsurance from reinsurer(s) Could be automatic (i.e., applies to the policy as part of a broad reinsured group) Could pertain to just that policy –Insured is not involved in the reinsurance transaction, and may not even be aware that reinsurance applies to her/his risk –“ Retrocession ” : a reinsurance transaction on already reinsured risks

5. 5 “ Layers ” of Responsibility Policyholder (or insured) –Responsible for losses within the deductible –Responsible for losses above the policy limit –Also responsible for any “ copayment ” Insurer (or “ ceding company ” ) –Collects premiums and pays losses according to the policy provisions –May cede some premium and loss to reinsurer(s) Reinsurer(s) –Reimburses insurer for reinsured payments

6. 6 Purposes and Functions of Reinsurance Catastrophe protection / limitation of liability –Possible bases of catastrophic limit application (from perspective of ceding company): Maximum payable on an individual risk Maximum payable for an individual event Maximum payable in the aggregate (e.g., per year) –Reduces impact of significant events

7. 7 Purposes and Functions of Reinsurance (cont.) Stabilization –Reduces variability of insurer results by “ smoothing out ” loss experience E.g., in catastrophe reinsurance, large loss peaks are reinsured – for a price

8. 8 Purposes and Functions of Reinsurance (cont.) Capacity –Insurer can take on more risk – e.g., write higher policy limits Financial management –Timing of certain accounting / cash flow items can be altered and managed

9. 9 Types of Reinsurance Treaty versus facultative –Treaty: a contract by which underlying insurance policies of a specified type are each subject to a reinsurance program –Facultative: reinsurance parameters (and whether reinsurance applies at all) are individually decided / negotiated for each underlying insurance policy

10. 10 Types of Reinsurance (cont.) Proportional (or “ pro rata ” ) versus Excess –Proportional Quota share – percentage sharing of business Surplus share –Excess Per Occurrence – for each loss, the reinsurer pays that portion of the loss above a certain dollar threshold (the ceding company ’ s “ retention ” ) Per risk Aggregate

11. 11 Issues Leveraged effect of inflation –Over time, more claims will trend, or inflate, into an excess reinsurance layer –Claims that are already above the retention will be further above the retention after inflation, with all of the additional cost of the claim going to the excess layer Collectibility of reinsurance Pricing of reinsurance –Time value of money is critical

12. 12 More Issues Ceding commissions Treatment of allocated loss adjustment expenses Quantities and terminology –Gross versus net –Subject premium –“ Inures to the benefit of ”

13. 13 2008 CAS Exam 6, Problem # 26

14. 14 2008 CAS Exam 6, Problem # 28

15. 15 2008 CAS Exam 6, Problem # 29

16. 16 2008 CAS Exam 6, Problem # 32

17. 17 2008 CAS Exam 6, Problem # 33