1. BENFIELD GREIG Long Term Reinsurance Buying Strategies modelled using a component based DFA Tool Astin July 2001

2. Introduction Investigate possible reinsurance strategies over several years. Two Strategies: Constant Cover, but vary premium spend. Constant Spend, but vary cover purchased. Use Monte Carlo Simulation to evaluate Risk / Return for an example company.

3. Reinsurance Pricing Factors Many potential ways to model changes in reinsurance pricing Various factors including:  Loss Experience  Changes in exposure  Reinsurance Market conditions The method used here is based on Loss Experience, with exposure and market factors assumed to be constant.

4. Example Company Example model is a property Cat XL programme with the following parameters (USD million):  Premium Income120  Expenses 30  Small Claims 48  Large Cat Loss FreqPoisson distribution with mean 1. Large Cat Loss SizeLognormal distribution, mean 12, standard dev. 16.

5. Example Company Reinsurance The reinsurance programme consists of 4 layers as follows: (USD million) All layers have 1 reinstatement at 100%. Initial coinsurance for all layers is 25%.

6. Different Strategies Each Layer considered Separately In Constant Cover strategies, coinsurance is fixed and premium paid varies. In Constant Spend strategies, coinsurance varies to keep premium spend constant.

7. Change in Reinsurance Pricing The price of each layer in the reinsurance programme will vary, with an increase in price if the experience account (EA) for the layer is negative, and a reduction in price if the EA is positive and there are no losses in the previous year. EA = reinsurance premiums and reinstatements – recoveries if EA < 0 then premium = previous premium + EA * 10% if EA > 0 then rate = previous rate * 90% Initial EA = 0.

9. Model Implentation Modelled Using ReMetrica II Component Based Framework for risk analysis and DFA ( Dynamic Financial Analysis ) Main Uses Include: – Reinsurance Pricing and Strategy – Risk Based Capital Modelling & Capital Allocation – Business Planning

10. The Model

11. Results The graphs below show the cedant’s net underwriting result. As a measure of risk we show:  Standard Deviation  1 in 100 result  Probability of a negative UW result As a measure of return we use expected UW result. The numbers on the graph indicate the years 1 – 5.

12. Results The results were based on 20,000 simulations using stratified sampling of 10,000 strata Performed sensitivity testing with further simulations ( 50,000 ) and different parameters.

13. Risk Return - Standard Deviation

14. Risk Return - 1 in 100

15. Risk Return - Probability Loss

16. Conclusions Constant Spend strategy better than Constant Cover Strategy. Return appears similar, but risk is less. Consistent across different risk measures.

17. Relevance Constant Spend strategy is similar to the following strategy: – Buy core programme down from a top PML ( probable maximum loss ) figure and buy lower down on an opportunistic basis. Opposite strategy reduces reinsurance when cost is low and buys more when costs are high. I call this the ‘short memory’ strategy. Constant Cover is neutral. This analysis indicates that buying down from your PML as far as your budget will allow is a good strategy. ( In practice, will still need a core programme. ) This analysis may help a reinsurance manager defend against the ‘short memory’ strategy.