1. r 12/6/2015, 1 The Role of Reinsurance in a Total Risk Management Program John Beckman Stephen Mildenhall CAS CARe Seminar Baltimore, June 1999

2. r 12/6/2015, 2 Overview ä Risks faced by an (re-)insurer (JB) ä Need for aggregate loss distributions (SM) ä Measures of risk (SM) ä Creating aggregate distributions (SM) ä Strategy design and implementation (JB)

3. r 12/6/2015, 3 Risks Faced by Insurers ä Lowe & Stanard (Spring 1996 Forum) risks faced by an insurance enterprise ä Liability Risk ä Asset Risk ä Business Risk

4. r 12/6/2015, 4 Risks Faced by Insurers ä Underwriting Risk ä Balance Sheet Risk ä Business Risk ä Organizational Risk

5. r 12/6/2015, 5 Aggregate Loss Distributions ä Analysis of risks shows understanding of liabilities is key ä Insurance liabilities variable in amount and timing ä Initial focus is on amount of loss ä Suggests an accident year ultimate view ä Future work to consider timing risk (see my upcoming DFA Seminar talk in Chicago)

6. r 12/6/2015, 6 Aggregate Loss Distributions ä Design criteria for producing aggregates ä Include all lines of business, all liabilities ä Appropriate treatment of catastrophes ä Capture correlation ä Within year, between line ä Between years

7. r 12/6/2015, 7 Aggregate Loss Distributions ä All lines of business ä Total risk management program must take portfolio view ä Achieving balance at department / business unit levels expensive and serves no economic purpose ä Risk fundamentally a question of aggregation

8. r 12/6/2015, 8 Aggregate Loss Distributions ä All lines of business ä Effect of adding uncorrelated risk on extreme percentiles is less than expected, especially after considering pricing ä Example: Expected loss ratio 80% on $375M premium, losses lognormal with CV 0.20 ä 99%ile loss ratio is 124% ä Add ILW type loss, 5% chance of $50M payout, 95% chance of $0M payout, priced at 50% loss ratio

9. r 12/6/2015, 9 Aggregate Loss Distributions ä Example continued ä ILW premium is $2.5M / 0.5 = $5.0M ä 99%ile losses increase by only $4.8M to $471M ä 99%ile loss ratio unchanged at 124% ä Shows combined effect of adding lower loss ratio business and portfolio effect on losses ä Computation is based on conditional probability: P(L+S<x) = P(L<x-s|S=s)P(S=s) + P(L<x|S=0)P(S=0) = 0.05 P(L<x-s) + 0.95 P(L<x) where L = base losses, S = added ILW losses

10. r 12/6/2015, 10 Aggregate Loss Distributions ä Catastrophes ä Major source of variability in liabilities ä Major source of correlation between lines of business ä Sophisticated models available to quantify amount and distribution of losses ä Recommend modeling cat losses separately from non-cat losses

11. r 12/6/2015, 11 Aggregate Loss Distributions ä Capture correlation ä Cat, discussed above ä Non-cat correlations in loss ratios largely driven by pricing (year-to-year) and property ä Beware statewide splits of data which introduce hard-to-model correlations ä One-year accident year plans can incorporate common pricing movements ä Allows realistic model of loss ratio

12. r 12/6/2015, 12 Measures of Risk ä Risk management process requires quantifiable measures of risk and setting targets for risk constraints ä Measures should capture solvency and stability constraints ä Solvency is related to probability of loss in excess of a key threshold, such as comb- ined ratio which would trigger down-grade

13. r 12/6/2015, 13 Measures of Risk ä Stability is desire for actual results to be reasonably close to plan ä Possible measures include variance, standard deviation, CV, down-side risk ä Percentile related measures more direct ä 1 year out of 10, combined ratio should be between plan + x and plan + y ä Lower bound is guide to suitable risk appetite

14. r 12/6/2015, 14 Measures of Risk ä Graphic illustrates constraints ä Stability is horizontal constraint ä Solvency is vertical constraint 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0%50%100%150%200% Combined Ratio F(Combined Ratio) Expected Combined 105% Solvency Constraint 95%ile<150% CR Stability Constraint Plan+10<90%ile<Plan+20 Combined Ratio Probability Distribution

15. r 12/6/2015, 15 Creating Aggregate Loss Distributions ä Many tools available for making aggregates ä See other sessions at CARe! ä Frequency and severity approach ä Stratify book by attachment and limit ä Model cats separately ä Method of moments to match three moments for large books

16. r 12/6/2015, 16 Creating Aggregate Loss Distributions ä Fast Fourier Transform methods ä Programming overhead to set up ä S. Wang Proceedings paper (www.casact.org) ä Simulation too slow ä Recursive methods more of academic interest and very computationally intensive

17. r 12/6/2015, 17 Creating Aggregate Loss Distributions ä Correlation between lines: use Iman- Conover shuffling method or other copula based method ä Again, see Wang’s paper ä Gives sample from multivariate distribution with desired correlation structure ä Easy to implement ä Can be done in Excel ä Basis for correlations in At Risk

18. r 12/6/2015, 18 Strategy Design ä GOAL: Maximize profit objective subject to risk constraints ä Requires quantifiable measures of risk ä Requires targets for risk constraints ä Requires structuring risk management program to meet targets ä Requires monitoring of performance against targets

19. r 12/6/2015, 19 Strategy Design ä Quantifiable Measures of Risk ä Solvency Measures ä Probability of Ruin ä Probability of Impairment ä Probability of Employment ä Stability Measures ä Probability of Combined Ratio > x% ä Probability of Exceeding Plan by y% ä Probability of Under Performing the Market by z%

20. r 12/6/2015, 20 Strategy Design ä Establishing Targets ä Structuring Risk Management Program ä Mix of Business ä Net Retained Lines ä Reinsurance! ä Implementation

21. r 12/6/2015, 21 Implementation ä Use of Reinsurance ä Have a defined purpose for reinsurance ä Promote Stability ä Promote Solvency ä There are other uses for reinsurance ä Evaluate the benefit provided versus the cost ä Continue to monitor performance against expectations

22. r 12/6/2015, 22 Reinsurance vs. Capital Markets ReinsuranceSecuritization Risk MatchingTailoredStandardized AccountingReinsuranceVaries/Complex Trans. ExpenseLowHigh Price????!